Question:
If sin θ + cosec θ = 2, then sin2θ + cosec2θ is equal to
A. 1
B.4
C. 2
D. None of these
Solution:
C. 2
Explanation:
According to the question,
sin θ + cosec θ = 2
Squaring LHS and RHS,
We get,
⇒ (sin θ + cosec θ)2 = 22
⇒ sin2θ + cosec2θ + 2 sin θ cosec θ = 4
⇒ sin2θ + cosec2θ + 2 sin θ (1/sin)θ = 4
⇒ sin2θ + cosec2θ + 2 = 4
⇒ sin2θ + cosec2θ = 2
Thus, option (C) 2 is the correct answer.