SSC CHSL 2021 PYQ — Question 53

The correct answer is option 3 i.e. $\frac{1}{3}$

Concept USed:

cos(90 - A) = sinA

tan(90 - A) = cotA

sin²A + cos²A = 1

cosec²A - cot²A = 1

Explanation:

According to the given question,

  $\frac{3 cos^2 27° - 5 + 3 cos^263°}{ tan^232° + 4 - cosec^258°}$ + sin35°cos55°+ cos35°sin55°

⇒  $\frac{3 cos^2 (90 - 63°) - 5 + 3 cos^263°}{ tan^2(90 - 58°) + 4 - cosec^258°}$ +sin(90 - 55°)cos55°+ cos(90 - 55°)sin55°

⇒ $\frac{3 sin^2 63° - 5 + 3 cos^263°}{ cot^258°+ 4 - cosec^258°}$+ cos55°cos55°+ sin55°sin55°

⇒ $\frac{3 (sin^2 63° + cos^263°) - 5}{ (cot^258° - cosec^258°) + 4}$+ cos²55°+ sin²55°

⇒ $\frac{3 - 5}{ -1 + 4}$+ 1

⇒ $\frac{-2}{3}$+ 1

 ⇒ $\frac{1}{3}$ 

Hence the required answer is $\frac{1}{3}$.