Question

hey plz help me!
it's request

Answer 1

$\bf{Given : (Tan\theta + \frac{1}{Cos\theta})^2 + (Tan\theta - \frac{1}{Cos\theta})^2}$

$\bf{\implies [Tan^2\theta + \frac{1}{Cos^2\theta} + 2Tan\theta(\frac{1}{Cos\theta})] + [Tan^2\theta + \frac{1}{Cos^2\theta} - 2Tan\theta(\frac{1}{Cos\theta})]}$

$\bf{\implies [Tan^2\theta + \frac{1}{Cos^2\theta}}] + [Tan^2\theta + \frac{1}{Cos^2\theta}]}$

$\bf{\implies [2Tan^2\theta + \frac{2}{Cos^2\theta}}]$

$\bf{\implies [\frac{2Sin^2\theta}{Cos^2\theta} + \frac{2}{Cos^2\theta}}]$

$\bf{\implies [\frac{2Sin^2\theta + 2}{Cos^2\theta}]$

$\bf{\implies [\frac{2(Sin^2\theta + 1)}{1 - Sin^2\theta}]$

Identities used to solve this problem :

✿ (a + b)² = a² + b² + 2ab

✿ (a - b)² = a² + b² - 2ab

✿ $\bf{Tan^2\theta = \frac{Sin^2\theta}{Cos^2\theta}}$

✿ Cos²θ = 1 - Sin²θ