The above expression cannot be expressed in an algebraic form.
The question contains an expression but not an equation. An expression cannot be solved.
sin[cos-1(x)] is an expression; it is not an equation (nor inequality). An expression cannot be solved.
Let y = sin(cos-1(2/5)) Suppose x = cos-1(2/5): that is, cos(x) = 2/5 then sin2(x) = 1 - cos2(x) = 1 - 4/25 = 21/25 so that sin(x) = sqrt(21)/5 which gives x = sin-1[sqrt(21)/5] Then y = sin(cos-1(2/5)) = sin(x) : since x = cos-1(2/5) =sin{sin-1[sqrt(21)/5]} = sqrt(21)/5 There will be other solutions that are cyclically related to this one but no range has been given for the solutions.
If cos(x) = 0 then the expression is undefined. Otherwise, it is T8.
Using the identity, sin(X)+sin(Y) = 2*sin[(x+y)/2]*cos[(x-y)/2] the expression becomes {2*sin[(23A-7A)/2]*cos[(23A+7A)/2]}/{2*sin[(2A+14A)/2]*cos[(2A-14A)/2]} = {2*sin(8A)*cos(15A)}/{2*sin(8A)*cos(-6A)} = cos(15A)/cos(-6A)} = cos(15A)/cos(6A)} since cos(-x) = cos(x) When A = pi/21, 15A = 15*pi/21 and 6A = 6*pi/21 = pi - 15pi/21 Therefore, cos(6A) = - cos(15A) and hence the expression = -1.
In algebra, capital letters are typically reserved for representing constants, while lowercase letters are used for variables. This convention helps distinguish between fixed numerical values and unknown quantities being studied. Using this consistent notation also helps avoid confusion and errors when working with algebraic expressions.
There are a couple: (1+SQRT(5))/2 1/(2*cos(72)) (degrees only)
The question contains an expression but not an equation. An expression cannot be solved.
sin[cos-1(x)] is an expression; it is not an equation (nor inequality). An expression cannot be solved.
Let y = sin(cos-1(2/5)) Suppose x = cos-1(2/5): that is, cos(x) = 2/5 then sin2(x) = 1 - cos2(x) = 1 - 4/25 = 21/25 so that sin(x) = sqrt(21)/5 which gives x = sin-1[sqrt(21)/5] Then y = sin(cos-1(2/5)) = sin(x) : since x = cos-1(2/5) =sin{sin-1[sqrt(21)/5]} = sqrt(21)/5 There will be other solutions that are cyclically related to this one but no range has been given for the solutions.
Remember that tan = sin/cos. So your expression is sin/cos times cos. That's sin(theta).
If cos(x) = 0 then the expression is undefined. Otherwise, it is T8.
cos(30)cos(55)+sin(30)sin(55)=cos(30-55) = cos(-25)=cos(25) Note: cos(a)=cos(-a) for any angle 'a'. cos(a)cos(b)+sin(a)sin(b)=cos(a-b) for any 'a' and 'b'.
cos(x) = 1 - x2/2! + x4/4! - x6/6! + ... where x is the angle measured in radians.
cos(t) - cos(t)*sin2(t) = cos(t)*[1 - sin2(t)] But [1 - sin2(t)] = cos2(t) So, the expression = cos(t)*cos2(t) = cos3(t)
cos x
Using the identity, sin(X)+sin(Y) = 2*sin[(x+y)/2]*cos[(x-y)/2] the expression becomes {2*sin[(23A-7A)/2]*cos[(23A+7A)/2]}/{2*sin[(2A+14A)/2]*cos[(2A-14A)/2]} = {2*sin(8A)*cos(15A)}/{2*sin(8A)*cos(-6A)} = cos(15A)/cos(-6A)} = cos(15A)/cos(6A)} since cos(-x) = cos(x) When A = pi/21, 15A = 15*pi/21 and 6A = 6*pi/21 = pi - 15pi/21 Therefore, cos(6A) = - cos(15A) and hence the expression = -1.