Question

3) Prove the following:
1- cos 2A /1+cos 2A = tan^2A​

Answer 1

SOLUTION:-

Given:

1-cos²A/1+cos2A = tan²A

Proof:

cos²A = 2cos²A -1

Take L.H.S

$= > \frac{1 - (2 {cos}^{2} A - 1)}{1 + (2 {cos}^{2} A - 1) } \\ \\ = > \frac{1 - 2cos {}^{2} A + 1 }{1 +2 {cos}^{2} A - 1 } \\ \\ = > \frac{2 - 2 {cos}^{2} A}{2 {cos}^{2} A } \\ \\ = > \frac{2(1 - {cos}^{2} A)}{2 {cos}^{2} A} \\ [{sin}^{2} A + {cos}^{2} A = 1] \\ = > 1 - {cos}^{2} A = {sin}^{2} A \\ \\ = > \frac{ {sin}^{2} A}{ {cos}^{2} A } \\ \\ = > {tan}^{2} A \: \: \: \: \: \: \: \: \: \: [R.H.S]$

Hence,

Proved.

Hope it helps ☺️

Answer 2

$\huge{\textbf{Solution is attached here.}}$