Question

Prove sin^2x - cos^2x=1-2cos^2x

Answer 1

Lhs=sin2x-cos2x

=1-cos2x-cos2x

=1-2cos2x

rhs=Lhs

Answer 2

sin²x - cos²x = 1 - 2cos²x

Here, we know the identity

sin²θ = 1 - cos²θ

Now,

sin²x - cos²x = 1 - 2cos²x

1 - cos²x - cos²x = 1 - 2cos²x

1 - 2cos²x = 1 - 2cos²x

L.H.S = R.H.S

Hence Proved!

-TheUnknownScientist 72