Question

Prove the following identity:

Sin A - 2 sin3 A / 2 cos3 A - cos A = tan A

Answer 1

It is given:

$\frac{sinA-2sin^3A}{2cos^3A-cosA}\\ =\frac{sinA(1-2sin^2A)}{cosA(2cos^2A-1)}\\ =tanA*\frac{1-2sin^2A}{2cos^2A-1}\\=tanA*\frac{1-2(1-cos^2A)}{2cos^2A-1}\\=tanA*\frac{1-2+2cos^2A}{2cos^2A-1}\\ =tanA*\frac{2cos^2A-1}{2cos^2A-1}\\ =tanA$

Therefore, it is proved.

Answer 2

Explanation:

To prove the above equation as Tan A, you need to follow the below procedure:

Sin A (1-sin2A)/Cos A (2Cos2A-1)

As per the formula = (sin2A+cos2A =1)

=Tan A (Cos2A-sin2A)/(cos2A-sin2A)

=Tan A

You can further discuss in your class or peer group to clear your doubts and have a better understanding of the same. Keep practicing more such exercise to brush your skills and learn such things.