If (sinθ + cosecθ)2 + (cosθ + secθ)2 = k + tan2θ + cot2θ, then the value of k is equal to:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 7
⇒ (sinθ + cosecθ)2 + (cosθ + secθ)2 = k + tan2θ + cot2θ
⇒ sin2θ + cosec2θ + 2sinθ × cosecθ + cos2θ + sec2θ + 2cosθ × secθ - tan2θ - cot2θ = k
⇒ 1 + 2 + 2 + cosec2θ - cot2θ + sec2θ - tan2θ = k
⇒ 5 + 1 + 1 = 7.