SSC CHSL 2021 PYQ — Question 57

The correct answer is Option 2 i.e. ${ \sqrt{3}}$

Concept Used:

sin(90 - A) = cosA

tan(90 - A) = cotA

sec(90 - A) = cosecA

Explanation:

According to the given question,

${{sin33°cos57°+sec62°sin28°+cos33°sin57°+cosec62°cos28°} \over tan15° tan35° tan60°tan55°tan75°}$

⇒ ${{sin(90 - 57°)cos57°+sec62°sin(90 - 62°)+cos(90 - 57°) sin57°+cosec(90 - 28°)cos28°} \over tan15° tan(90 - 55°) tan60°tan55°tan(90 - 15°)}$

⇒ ${{cos57°​​cos57°+sec62°cos62°+sin57°sin57°+sec28°cos28°} \over tan15° cot55° tan60°tan55°cot15°}$

⇒ ${{​​cos^257°+1+sin^257°+ 1} \over tan60°}$

⇒ ${3 \over \sqrt{3}}$ = ${ \sqrt{3}}$

Hence the required answer is ${ \sqrt{3}}$.