Question

prove that cos 2x+2sinsquarex=1

Answer 1

Hello users......

We have to prove that

Cos 2x + 2 sin² x =1

Solution:-

We know that
Cos(x+y) = cos x cos y - sin x sin y
And
Sin ² x+ cos ² x = 1

Here
Cos 2x = cos (x+x) = cos xcosx - sin x sin x
= Cos ² x - sin ² x

Now taking LHS
Cos 2x + 2 sin² x
= (Cos ² x - sin ² x ) + 2sin² x
= Cos ² x + sin ² x = 1 = RHS

⭐⭐ hope it helps ⭐⭐