What is the value of cos2180x sin2180x for any real number

What is the value of cos^2(180x) + sin^2(180x) for any real number x? It cannot be determined because it depends on x. 0 1 -1 None of the above. Simplify the expression = cos^2(x) -1/sin(x) sin^3(x) sin^2(x) cos(x) -sin (x) None of the above. if f(t) is a trigonometric function such that (f(t))^2 = sec(t) - cos(t)/sec (t), then what is f(t)? sin(t) cos(t) sec(f) csc(t) None of the above. Without using a calculator to find the value for cos(396 degree) cos (126 degree) + sin (396 degree) sin (126 degree). 1.2345 0 -1.051 -1.052 None of the above.

Solution

13. cos²180x + sin²180x

According to pythagoras identity

cos²theta + sin²theta=1

Therefore

cos²180x + sin²180x=1

Hence the correct option is c.

14. (cos²x-1)/sinx

According to pythagoras identity

cos²x=1-sin²x

(1 - sin²x-1)/sinx= -sin²x/sinx = -sinx

Hence the correct option is D

15. f(t)²= (sec t - cos t)/sec t

     f(t)²= (1/cost     - cost)/1/cos t

     f(t)²= (1-cos²t)=sin²t

     f(t)²=sin²t

     f(t)=sin t

Hence the correct option is A

16.   cos 396 cos 126 + sin 396 sin 126

This is of the form

cos A cos B +sinA sin B= cos(A-B)

Therefore cos 396 cos 126+ sin 396 sin 126= cos(396-126)=cos 270=0

Hence the correct option is B