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If 4(cosec2 57 - tan2 33) - cos 90 + y × tan2 66 × tan24 = y/2, then the value of y is:  
1. 8
2. -4
3. 4
4. -8

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Correct Answer - Option 4 : -8

Given:

4(cosec2 57 - tan2 33) - cos 90 + y × tan2 66 × tan24 = 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/tan66 = y/2

⇒ 4 + y = y/2

⇒ y - y/2 = -4

⇒ y/2 = -4

⇒ y = -8

∴ The value of y is -8.

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