Question

If f(x) = sin x and F(x) = cos x , prove that
(1) [f(x)]^2 + [F(x)]^2 = 1
(ii) f (2x) = 2 f (x).F(x) ​

Answer 1

Given,

f(x) = sin x  and F(x) = cos x

To prove:  [f(x)]² + [F(x)]² = 1

(sin x)² + (cos x)² = 1

sin² x + cos² x = 1

1 = 1

L.H.S = R.H.S

Hence proved.

In trigonometry sin 2x = 2sinxcosx

Here given,

f(2x) = 2f(x)F(x)

sin(2x) = 2sinxcosx

Hence proved.