Question

prove that
SinA+Sin3A/cosA+cos3A
= tan2a​

Answer 1

LHS:. Sin A + sin3A/Cos A +Cos 3A

Sin A + 3Sin A - 4sin³ / Cos A + 4cos³ - 3cos A

4sinA - 4sin³/ 4cos³A - 2cos A

4SinA ( 1- sin² ) / 2 cosA ( 2cos²A - 1)

2sinA (cos²A) / cosA (cos2A)

2 sinA(cosA) / cos 2A

Sin2A/cos2A

Tan 2A =RHS

hence proved