SSC CHSL 2023 PYQ — Question 56

The correct answer is option 4 i.e. sin²Ø.

$\frac{(1 + \sec Ø)}{\secØ} (1 - \cosØ)$

$=\frac{(1 + \frac{1}{\cos Ø})}{\frac{1}{\cos Ø}} (1 - \cosØ)$

$=\frac{\frac{cosØ+1}{cosØ}}{\frac{1}{cosØ}}(1 - \cos Ø)$

$=(\cos Ø + 1) (1 - \cosØ)$

= 1 - cos²Ø

= sin²Ø

Hence, the value of the expression is sin²Ø.