Correct Answer - Option 2 :
\(\dfrac{8}{3}\)
Given:
4(cosec2 57° – tan2 33°) - cos 90° – y tan2 66° tan2 24° \(=\dfrac{y}{2}\)
Formula used:
cosec2θ – cot2θ = 1
tan(90 – θ) = cotθ
Calculation:
4(cosec2 57° – tan2 33°) – cos 90° – y tan2 66° tan2 24° \(=\dfrac{y}{2}\)
⇒ 4[cosec2 57° – cot2(90° – 33°)] – cos 90° – y tan2 66° cot2(90° – 24°) \(=\dfrac{y}{2}\)
⇒ 4(cosec2 57° – cot2 57°) – cos 90° – y tan2 66° cot2 66° \(=\dfrac{y}{2}\)
⇒ 4 – 0 – y = y/2
⇒ 8 = 3y
⇒ y = 8/3
∴ The value of y is 8/3.