If 4(cosec2 57 - tan2 33) - cos 90 + y × tan2 66 × tan2 24 = y

1.	If 4(cosec2 57 - tan2 33) - cos 90 + y × tan2 66 × tan2 24 = y/2, then the value of y is: 1. 82. -43. 44. -8
Answer» 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.

If 4(cosec2 57 - tan2 33) - cos 90 + y × tan2 66 × tan2 24 = y/2, then the value of y is: 1. 82. -43. 44. -8

Answer» 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.