SSC CGL 2021 PYQ — Question 53

The correct answer is option 2 i.e. 1

Here it is given that,

 = sec⁴$\theta$(1 - sin⁴$\theta$) - 2tan²$\theta$  

= 1/cos⁴$\theta$( 1 - (sin²$\theta$)²) - 2 × sin²$\theta$/cos²$\theta$

= 1/cos²$\theta$(1 - sin²$\theta$) × (1 + sin²$\theta$)(1 - sin²$\theta$) -  2 × sin²$\theta$/cos²$\theta$

=  (1 + sin²$\theta$)/ cos²$\theta$  -   2 × sin²$\theta$/cos²$\theta$

= ( 1 + sin²$\theta$ - 2sin²$\theta$)/ cos²$\theta$

=  cos²$\theta$/ cos²$\theta$

= 1.