If sin(20 +x)º = cos 60º, 0 ≤ (20 + x) ≤ 90, then find the value of 2sin²(3x + 15)º - cosec²(2x+10)º.

If sin(20 +x)º = cos 60º, 0 ≤ (20 + x) ≤ 90…

If sin(20 +x)º = cos 60º, 0 $\leq$ (20 + x) $\leq$ 90, then find the value of 2sin²(3x + 15)º - cosec²(2x+10)º.

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Correct answer: B

Explanation

The correct answer is option 2 i.e. -3.

One knows that,

Sin30° = Cos60°

20 + x = 30

x = 10°.

⇒ 2sin²(3x + 15)º cosec²(2x+10)º = 2sin²(3 × 10 + 15) - cosec²(2 × 10 + 10)

⇒ 2 × 1/2 - 4 = -3.