SSC CGL Tier II - Quant - 3 Feb 2022

 The correct answer is option 4 i.e. 2

Sin( 90 - $\theta$) = cos$\theta$.$\theta$

Sec( 90 - $\theta$) = cosec$\theta$.

Sec²$\theta$ - tan²$\theta$ = 1

= $\frac{(cos 9^0+sin 81^0)(sec9^0+cosec81^0)}{cosec^271^0+cos^215^0-tan^219^0+cos^275^0}$

= $\frac{(sin81^0+sin 81^0)(cosec81^0+cosec81^0)}{sec^219^0+sin^275^0-tan^219^0+cos^275^0}$

= (2 × 2)/2 = 2.