Question

Find the value of [2 + sec²A - cot²(90° - A)] × [tan²(90° - A) × (1/cot ²A)]
1. 3
2. 1
3. 4
4. 7

Answer 1

Correct Answer - Option 1 : 3

Given

[2 + sec2A - cot2(90° - A)] × [tan2(90° - A) × (1/cot 2A)]

Formula used

cot(90° - A) = tan A

tan(90° - A) = cot A

Calculation

[2 + sec2A - cot2(90° - A)] × [tan2(90° - A) × (1/cot 2A)]

= [2 + sec²A - tan ²A] × (cot ²A) × (1/cot ²A)

⇒ (2 + 1) × 1

⇒ 3 × 1

⇒ 3

∴ [2 + sec2A - cot2(90° - A)] × [tan2(90° - A) × (1/cot 2A)] is 3