Question

using the formula of Sin 2A ,cos2a and tan 2a establish that; tab A is = +- root under 1 - cos 2A by 1 + cos 2a​

Answer 1

Explanation:

Given identity is,

`\text{tanA}=\pm\sqrt{\frac{1-\text{cos2A}}{1+\text{cos2A}}}`

To prove this identity, we will take left side of the identity,

`\pm\sqrt{\frac{1-\text{cos2A}}{1+\text{cos2A}}}=\pm\sqrt{\frac{1-(1-2\text{sin}^2A)}{1+(2\text{cos}^2A-1)} }`

`=\pm\sqrt{\frac{1-1+2\text{sin}^2A}{1+2\text{cos}^2A-1} }`

`=\pm\sqrt{\frac{2\text{sin}^2A}{2\text{cos}^2A} }`

`=\pm(\sqrt{\text{tan}^2A})`

`=\text{tanA}` [Right side of the identity]

Hence, proved.