Convert the cos 2A in the numerator to 1 - 2 sin^2 A.

Convert the cos 2A in the denominator to 2 cos^2 A - 1.

Simplify after that.

You should get your answer soon thereafter.

thanks :-)

cos 2A has three equivalent forms.

The original form, cos^2 A - sin^2 A, is good for factorisation purposes.

The two modified forms are useful to convert expressions into sine only or cosine only expressions and are thus suitable for solving trigonometric equations involving cos 2A.

In this particular case for proving, I pick the format which allows me to eliminate the “1” in each scenario - choosing the sine only form allows me to remove the “1” in the numerator, while choosing the cosine only form allows me to remove the “1” in the denominator.

This is important because we find it difficult to divide fractions with two terms in the denominator, so we find a way to convert the denominator into a single term expression.