Verified answer

cos^2(P) + sin^2(P) = 1

cos^2(P) = 1 - sin^2(P)

Substituting this into cos^2(P) - sin^2(P) gives

1 - sin^2(P) - sin^2(P) = 1 - 2sin^2(P)

cos²θ - sin²θ = 1 - 2sin²θ

Note: θ = theta

~~~~~~~~~~~~~~~~~~~~~~~~~~

METHOD: FROM LHS TO RHS

~~~~~~~~~~~~~~~~~~~~~~~~~~

Take the LHS.

cos²θ - sin²θ =

Remember that cos²θ = 1 - sin²θ.

1 - sin²θ - sin²θ =

Simplify.

1 - 2sin²θ

RHS

~~~~~~~~~~~~~~~~~~~~~~~~~~

METHOD: FROM RHS TO LHS

~~~~~~~~~~~~~~~~~~~~~~~~~~

Take the RHS.

1 - 2sin²θ =

Remember that sin²θ + cos²θ = 1.

sin²θ + cos²θ - 2sin²θ =

Simplify.

cos²θ - sin²θ =

LHS