SSC CGL 2021 PYQ — Question 52

The correct answer is option 1 i.e. 0

⇒ $(sec \theta + tan \theta) ^2 + \frac{1+cosec\theta }{1-cosec\theta}$

⇒ [(1/cos$\theta$) + sin$\theta$/cos$\theta$]² - $\frac{cosec\theta + 1 }{cosec\theta - 1}$

 ⇒ [(1 + sin$\theta$)/ cos$\theta$]² - $\frac{1 + sin\theta }{1 - sin\theta}$

 ⇒ [(1 + sin$\theta$)/ cos$\theta$]² - $\frac{1 + sin\theta }{1 - sin\theta}\times \frac{1 + sin\theta }{1+sin\theta}$

 ⇒ [(1 + sin$\theta$)/ cos$\theta$]² - $\frac{(1 + sin\theta)^2 }{(1 - sin^2\theta)}$

 ⇒ [(1 + sin$\theta$)/ cos$\theta$]² - [(1 + sin$\theta$)/ cos$\theta$]²  = 0