Question

sinA-2sin^3A/2cos^3A-cosA​

Answer 1

Answer:tan a

Step-by-step explanation: sin a - 2 sin³a / 2 cos³a - cos a

= sin a (1-2 sin²a) / cos a (2 cos²a - 1)

= sin a (1-sin²a-sin²a) / cos a (cos²a+cos²a-1)

Then (1-sin²a = cos²a) and (cos²a-1 = -sin²a)

= sin a (cos²a-sin²a) / cos a (cos²a-sin²a)

Canceling (cos²a-sin²a) on both numerator and denominator.

= sin a / cos a

= tan a