If 4(cosec2 57 – tan2 33) – cos 90 + y × tan2 66 × tan2 24 = y/2, then the value of y is:
1. 8
2. -4
3. 4
4. -8
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 × 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.