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## Related Questions

###### Asked in Math and Arithmetic, Algebra, Calculus

### How do you prove that (1 plus cotx)2-2cotx 1(1-cos)(1 plus cos)?

Manipulate normally, noting:
cot x = cos x / sin x
cos² x + sin² x = 1 → sin²x = 1 - cos² x
a² - b² = (a + b)(a - b)
1 = 1²
ab = ba
a/(bc) = a/b/c
(1 + cot x)² - 2 cot x = 1² + 2 cot x + cot² x - 2 cot x
= 1 + cot² x
= 1 + (cos x / sin x)²
= 1 + cos² x / sin² x
=...

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###### Asked in Math and Arithmetic, Algebra, Calculus

### What is sec x cos x?

sec x = 1/cos x
sec x cos x = [1/cos x] [cos x] = 1

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###### Asked in Calculus

### How do you solve sinx divided by 1 plus cosx plus cosx divided by sinx?

sin x/(1+cos x) + cos x / sin x
Multiply by sin x (1+cos x)
=[(sin^2 x + cos x(1+cos x) ] / sin x (1+cos x)
= [(sin^2 x + cos x + cos^2 x) ] / sin x (1+cos x)
sin^2 x + cos^2 x = 1
= (1+cos x) / sin x (1+cos x)
= 1/sin x
...

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###### Asked in Math and Arithmetic

### What does cosx divided by 1-sinx equal?

cos x / (1-sin x) = cos x (1 + sin x) / (1 - sin x) (1 + sin x)
= cos x (1 + sin x) / (1 - sin2x) = cos x (1 + sin x) / cos2 x = (1
+ sin x) / cos x = sec x + tan x
cos x / (1-sin x) = cos x (1 + sin x) / (1 - sin x) (1 + sin x) =
cos...

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###### Asked in Math and Arithmetic, Algebra, Calculus

### Prove each Indentity tanx mins sinx divided by tanxsinx equals tanxsinx divided by tanx plus sinx?

(tan x - sin x)/(tan x sin x) = (tan x sin
x)/(tan x + sin x)
[sin x/cos x) - sin x]/[(sin x/cos x)sin x] =?
[(sin x/cos x)sin x]/[sin x/cos x) + sin x]
[(sin x - sin x cos x)/cos x]/(sin2 x/cos x) =? (sin2 x/cos
x)/[(sin x + sin x cos x)/cos x)
(sin x - sin x cos x)/sin2 x =? sin2 x/(sin x + sin x cos x)
[sin x(1 - cos x)]/sin2 x =? sin2...

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###### Asked in Math and Arithmetic, Algebra, Calculus

### What is the integral of 1 divided by sin x plus cos x?

The question is ambiguous: does it refer to 1/sin(x) + cos(x) or
to 1/[sin(x)+cos(x)]?
The question is ambiguous: does it refer to 1/sin(x) + cos(x) or to
1/[sin(x)+cos(x)]?
The question is ambiguous: does it refer to 1/sin(x) + cos(x) or to
1/[sin(x)+cos(x)]?
The question is ambiguous: does it refer to 1/sin(x) + cos(x) or to
1/[sin(x)+cos(x)]?
...

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###### Asked in Trigonometry

### How does sin2x divided by 1-cosx equal 1 plus cosx?

sin2x / (1-cos x) = (1-cos2x) / (1-cos x) = (1-cos x)(1+cos x) /
(1-cos x) = (1+cos x)
sin2x=1-cos2x as sin2x+cos2x=1
1-cos2x = (1-cos x)(1+cos x) as a2-b2=(a-b)(a+b)
...

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###### Asked in Algebra, Trigonometry

### Sin x divided by 1 minus cos x equals csc plus cot x?

It helps to convert this kind of equation into one that has only
sines and cosines, by using the basic definitions of the other
functions in terms of sines and cosines.
sin x / (1 - cos x) = csc x + cot x
sin x / (1 - cos x) = 1 / sin x + cos x / sin x
Now it should be easy to do some simplifications:
sin x / (1 - cos x) = (1 +...

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###### Asked in Algebra, Calculus, Trigonometry

### What is Cos 2 x divided by cos x?

cos 2x = cos2 x - sin2 x
= 2 cos2 x - 1; whence,
cos 2x / cos x = 2 cos x - (1 / cos x)
= 2 cos x - sec x.
...

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###### Asked in Calculus

### What is (1 plus cos x)(1- cos x)?

(1+cosx)(1-cosx)= 1 +cosx - cosx -cos^2x (where ^2 means
squared)
= 1-cos^2x = sin^2x (sin squared x)
...

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###### Asked in Math and Arithmetic

### Limit when x goes to 0 tanx divided by x?

tan x = sin x / cos x, so:
lim (tan x / x) = lim (sin x / x cos x). Since it is known that
the limit of sin x / x = 1, you have lim 1 / cos x = 1 (since cos 0
= 1).
...

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###### Asked in Calculus, Math and Arithmetic, Algebra

### How do you find sec x cos x?

sec x = 1/cos x so sec x * cos x = 1

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###### Asked in Math and Arithmetic, Algebra, Calculus

### How do you prove tan x plus tan x sec 2x equals tan 2x?

tan x + (tan x)(sec 2x) = tan 2x work dependently on the
left side
tan x + (tan x)(sec 2x); factor out tan x
= tan x(1 + sec 2x); sec 2x = 1/cos 2x
= tan x(1 + 1/cos 2x); LCD = cos 2x
= tan x[cos 2x + 1)/cos 2x]; tan x = sin x/cos x and cos 2x = 1
- 2 sin2 x
= (sin x/cos x)[(1 - 2sin2 x + 1)/cos 2x]
= (sin x/cos x)[2(1 -...

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###### Asked in Calculus, Trigonometry

### Solution for tan x plus cot x divided by sec x csc x?

(tan x + cot x)/sec x . csc x
The key to solve this question is to turn tan x, cot x, sec x,
csc x into the simpler form.
Remember that tan x = sin x / cos x, cot x = 1/tan x, sec x =
1/cos x, csc x = 1/sin x
The solution is:
[(sin x / cos x)+(cos x / sin x)] / (1/cos x . 1/sin x)
[(sin x . sin x + cos x ....

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###### Asked in Math and Arithmetic, Algebra, Calculus

### How do you show that 2 sin squared x minus 1 divided by sin x minus cos x equals sin x plus cos x?

(2 sin^2 x - 1)/(sin x - cos x) = sin x + cos x
(sin^2 x + sin^2 x - 1)/(sin x - cos x) =? sin x + cos x
[sin^2 x - (1 - sin^2 x)]/(sin x - cos x) =? sin x + cos x
(sin^2 x - cos^2 x)/(sin x - cos x) =? sin x + cos x
[(sin x - cos x)(sin x + cos x)]/(sin x - cos x) =? sin...

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###### Asked in Math and Arithmetic, Algebra

### Cos x - cos x sin2 x equals cos3x?

cos(x)-cos(x)sin2(x)=[cos(x)][1-sin2(x)]
cos(x)-cos(x)sin2(x)=[cos(x)][cos2(x)]
cos(x)-cos(x)sin2(x)=cos3(x)
...

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###### Asked in Calculus, Trigonometry

### How many solutions does cos squared minus two cos equal three?

One solution.
(cos x)2 - 2cos x = 3
Factor:
(cos x - 3)(cos x + 1)= 0
cos x = {-1, 3}
Solve:
For cos x = -1, x = 180 deg
No solution for cos x = 3
...

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###### Asked in Math and Arithmetic, Algebra, Calculus, Trigonometry

### What is the deivative of 1 divided by cos x?

Rewrite 1/cos x as (cos x)-1 and use chain rule.

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###### Asked in Math and Arithmetic, Algebra, Calculus

### What is the derivative of cos x sin x divided by cos x sin x?

(cos x sin x) / (cos x sin x) = 1. The derivative of a constant,
such as 1, is zero.
...

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###### Asked in Math and Arithmetic, Algebra, Calculus

### Sec - cos equals tansin?

Prove that tan(x)sin(x) = sec(x)-cos(x)
tan(x)sin(x) = [sin(x) / cos (x)] sin(x)
= sin2(x) / cos(x)
= [1-cos2(x)] / cos(x)
= 1/cos(x) - cos2(x)/ cos(x)
= sec(x)-cos(x)
Q.E.D
...

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###### Asked in Math and Arithmetic, Algebra, Calculus

### Integral of cos x cot x?

cos(x) cot(x) = cos(x) * 1/(tan(x)) = cos(x) * 1 / (sinx(x) /
cos(x))
= cos2(x) / sin(x) = (1-sin2(x)) / sin(x) = 1/sin(x) -
sin(x)
so the antiderivative of cos(x)cot(x) =
log[abs(tan(x/2))]+cos(x)
This can also be written as log[abs((sin(x)/(cos(x)+1))]+cos(x)
if we want everything in terms of x and not (x/2). The two answers
are, of course, the same.
where log(x) refers to the natural log, often written ln(x).
We might write ln[|sin(x)|/|cos(x)+1|] +cos(x)
...

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###### Asked in Math and Arithmetic, Algebra, Calculus, Trigonometry

### What equals 1 - cos squared x divided by cos squared x?

tan^2(x)
Proof:
cos^2(x)+sin^2(x)=1 (Modified Pythagorean theorem)
sin^2(x)=1-cos^2(x) (Property of subtraction)
cos^2(x)-1/cos^2(x)=?
sin^2(x)/cos^2(x)=? (Property of substitution)
sin(x)/cos(x) * sin(x)/cos(x) = tan(x) * tan(x) (Definition of
tanget)
= tan^2(x)
...

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###### Asked in Math and Arithmetic, Algebra, Calculus

### How do you solve the following identity sec x - cos x equals sin x tan x?

sec x - cos x = (sin x)(tan x)
1/cos x - cos x = Cofunction Identity, sec x = 1/cos x.
(1-cos^2 x)/cos x = Subtract the fractions.
(sin^2 x)/cos x = Pythagorean Identity, 1-cos^2 x = sin^2 x.
sin x (sin x)/(cos x) = Factor out sin x.
(sin x)(tan x) = (sin x)(tan x) Cofunction Identity, (sin
x)/(cos x) = tan x.
...

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###### Asked in Math and Arithmetic, Algebra, Calculus

### Find the domain and range of sin x - cos x?

sin(x)-cos(x) = (1)sin(x)+(-1)cos(x)
so the range is sqrt((1)^2+(-1)^2)=1
and the domain is R
<><><><><>
The domain of sin x - cos x is [-infinity, +infinity].
The range of sin x - cos x is [-1.414, +1.414].
...

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###### Asked in Trigonometry

### Solution for tan x is equal to cos x?

if tan x = cos x then
sin x / cos x = cos x
=> sin x = cos x cos x
=> sin x = cos2 x
=> sin x = 1 - sin2x
=> sin2x + sin x - 1 = 0
Using the quadratic formula
=> 1. sin x = 0.61803398874989484820458683436564
=> x = sin-1 (0.61803398874989484820458683436564)
or
=> 2. sin x = -1.6180339887498948482045868343656
=> x = sin-1 (-1.6180339887498948482045868343656)
...

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