If 4 (cosec²57° - tan²33°) - cos90° - y tan² 66°tan²24° = y/2 , the value of y is :

If 4 (cosec²57° - tan²33°) - cos90° - y tan² 66°tan²24° =…

If 4 (cosec²57° - tan²33°) - cos90° - y tan² 66°tan²24° = $\frac{y}{2}$ , the value of y is :

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Correct answer: D

Explanation

The correct answer is option 4 i.e. $\frac{8}{3}$

4(cosec²57^o - tan²33^o) - cos 90^o - y tan²66^o tan²24^o = y/2

cosec²θ - cot²θ = 1

tan(90 - θ) = cotθ

4(cosec²57^o - tan²33^o) - cos 90^o - y tan²66^o tan²24^o= y/2

4[cosec²57^o - cot²(90^o - 33^o)] - cos 90^o - y tan²66^o cot²(90^o - 24^o) = y/2

4(cosec²57^o - cot²57^o) - cos 90^o - y tan²66^o cot²66^o = y/2

4 - 0 - y = y/2

8 = 3y

y = 8/3