# If f(sin x) = cos 2x, find f(cos x).

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It is given that f(sin x) = cos 2x. We have to determine f(cos x)

cos x = sin (90 - x)

f(sin (90 - x)) = cos (2*(90 - x))

=> cos (180 - 2x)

=> -cos 2x

**For the given function, f(cos x) = -cos 2x**

By the basic trigonometry we know that cosx=sin(90-x)

so put x=90-x in the function

f(sin x) = cos 2x

f(sin(90-x)=cos2(90-x)

f(cos x)=cos(180-2x)

now cos(x)=-cos(pie -x)

so f(cos x)=-cos2x.

this problem is similar to Algebra equations after we have inserted the value of x as 90-x

We have to determine f(cos x) cos x = sin (90 - x) f(sin (90 - x)) = cos (2*(90 - x)) => cos (180 - 2x) => -cos 2x For the given function, f(cos x) = -cos 2x