Correct Answer - Option 4 : -8
Given:
4(cosec2 57 - tan2 33) - cos 90 + y × tan2 66 × tan2 24 = y/2
Formula used:
(i) cosec(90 - θ) = secθ
(ii) tan(90 - θ) = cotθ
(iii) sec2θ - tan2θ = 1
(iv) tanθ = 1/cotθ
Calculations:
4(cosec2 (90 - 33) - tan2 33) - cos 90 + y × tan2 66 × tan2 (90 - 66) = y/2
⇒ 4(sec2 57 - tan2 33) - cos 90 + y × tan2 66 × cot2 66 = y/2
⇒ 4 × 1 - 0 + y × tan2 66 × 1/tan2 66 = y/2
⇒ 4 + y = y/2
⇒ y - y/2 = -4
⇒ y/2 = -4
⇒ y = -8
∴ The value of y is -8.