What is the value of 1/(sin⁴ (90^° - 2α)) + 1/(cos^2 (90^° - 2 α)-1)?

What is the value of 1/(sin⁴ (90^° - 2α)) + 1/(cos^2 (90^°…

What is the value of $\frac{1}{\sin^4 (90^\circ - 2\alpha)} + \frac{1}{\cos^2 (90^\circ - 2 \alpha)-1}?$

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Correct answer: B

Explanation

The correct answer is option 2 i.e. $\sec^2 2 \alpha \tan^2 2 \alpha$ .

⇒ 1/sin⁴(90° - 2α) + 1/(cos²(90° - 2α) - 1)

⇒ 1/cos⁴2α + 1/(sin²2α - 1)

Now, use the identity sin²(θ) - 1 = -cos²(θ):

⇒ 1/cos⁴2α + 1/-cos²(2α)

⇒ 1/cos⁴2α - 1/cos²(2α)

⇒ (1 - cos²2α)/cos⁴2α

⇒ sin²2α/cos⁴2α

⇒ tan²2α.sec²2α

Therefore, the value of the expression is tan²2α sec²2α.