# If tan y equals to x where y is acute find 3 cos y in terms of x?

3cos(y) = 3/(sqrt(1+x^2)

### Solve the equation 3cosx equals 2 for 0dgrees x 360degrees?

To solve this equation, you must first put the equation in terms of cosx. 3cosx=2 cosx = 2/3 Next, you find the reference angle (α) by finding the cos inverse of 2/3. α=cos-1(2/3) = 48.19 Degrees (approximately) find the distance from from 48.19 and 90 you then add the difference to 270 giving you the two answers which are ... 48.19 and 311.81 (approximately)

### Cos plus tansin equals sec?

Start on the left-hand side. cos(x) + tan(x)sin(x) Put tan(x) in terms of sin(x) and cos(x). cos(x) + [sin(x)/cos(x)]sin(x) Multiply. cos(x) + sin2(x)/cos(x) Make the denominators equal. cos2(x)/cos(x) + sin2(x)/cos(x) Add. [cos2(x) + sin2(x)]/cos(x) Use the Pythagorean Theorem to simplify. 1/cos(x) Since 1/cos(x) is the same as sec(x)- the right-hand side- the proof is complete.

### Find dy over dx in terms of x and y if cos to the power 2 braket 6yclose bracket plus sin to the power to open bracket 6y close bracket equals y plus 14?

Note : sin² Φ + cos² Φ = 1 for all real Φ. __________________________________ Now, given that : cos² (6y) + sin² (6y) = y + 14 ∴ 1 = y + 14 ∴differentiating w.r.t. x, ... 0 = (dy/dx) + 0 ∴ dy/dx = 0 ........... Ans. ___________________________________ Happy To Help ! ___________________________________

### How do you find out the shaded area of the graphs y equals sin x and y equals cosine x?

You find the value of the integral of the difference cos x - sin x between the limits of the shaded area. Note that if some of the area is below the x-axis when both cos x and sin x are less than 0, then the area will be negative and could result in a total area of zero (for example if the limits are 0 to 2π which results in a complete cycle of…

### How would you prove left cosA plus sinA right times left cos2A plus sin2A right equals cosA plus sin3A?

You need to make use of the formulae for sin(A+B) and cos(A+B), and that cos is an even function: sin(A+B) = cos A sin B + sin A cos B cos(A+B) = cos A cos B - sin A sin B cos even fn → cos(-x) = cos(x) To prove: (cos A + sin A)(cos 2A + sin 2A) = cos A + sin 3A The steps are to work with the left hand side…

### How do you prove that the sin over one minus the cosine minus one plus the cosine over the sine equals zero?

Multiply both sides by sin(1-cos) and you lose the denominators and get (sin squared) minus 1+cos times 1-cos. Then multiply out (i.e. expand) 1+cos times 1-cos, which will of course give the difference of two squares: 1 - (cos squared). (because the cross terms cancel out.) (This is diff of 2 squares because 1 is the square of 1.) And so you get (sin squared) - (1 - (cos squared)) = (sin squared) + (cos…

### How do you solve trignometric identities?

tan(x) = sin(x)/cos(x) Therefore, all trigonometric ratios can be expressed in terms of sin and cos. So the identity can be rewritten in terms of sin and cos. Then there are only two "tools": sin^2(x) + cos^2(x) = 1 and sin(x) = cos(pi/2 - x) Suitable use of these will enable you to prove the identity.