If cosθ.cosec23° = 1, the value of θ is?

A. 23°

B. 37°

C. 63°

D. 67°

Answer: Option D

Solution(By Examveda Team)

$$\eqalign{ & {\text{cos}}\theta .{\text{cosec2}}{{\text{3}}^ \circ } = {\text{1}} \cr & {\text{If cosA}}.{\text{cosecB}} = {\text{1}} \cr & {\text{Then, A + B}} = {90^ \circ } \cr & {\text{So,}} \cr & \theta {\text{ + 2}}{{\text{3}}^ \circ } = {90^ \circ } \cr & \theta = {67^ \circ } \cr} $$