Question in a trigonometric equation. (1-sin A)/(1+ sin A) = 1 + 2 tan A (tan A - sec A )

Hanna Webster 2022-11-20 Answered
Question in a trigonometric equation.
I tried it a lot but am not able to get this.Pls help in how should I think when solving this type of question and which side is better to try to simplify first (LHS or RHS).Please share the solution in that way.
1 sin A 1 + sin A = 1 + 2 tan A ( tan A sec A )
One of the ways I tried but am not understand that how to simplify it in such a way that you get the RHS?
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Answers (1)

Brooklyn Mcintyre
Answered 2022-11-21 Author has 18 answers
Starting from the LHS we have
1 sin ( A ) 1 + sin ( A )
= 1 sin ( A ) 1 + sin ( A ) 1 sin ( A ) 1 sin ( A ) = 1 2 sin ( A ) + sin 2 ( A ) 1 sin 2 ( A )
= cos 2 ( A ) 2 sin ( A ) + 2 sin 2 ( A ) cos 2 ( A )
using the identity sin 2 ( A ) + cos 2 ( A ) = 1. Can you end it now?
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