Question

if 4sin^2 A =1 then the value of 2+3cos^2A/1-2sin^2A​

Answer 1

Solution

→ 4 sin²A = 1

→ sin²A = ¼

Since we know identity sin²A + cos²A = 1, hence cos²A = 1 - sin²A.

→ (2 + 3 cos²A)/(1 - 2 sin²A)

→ [2 + 3(1 - sin²A)]/(1 - 2 sin²A)

→ [2 + 3 - 2 sin²A]/(1 - 2 sin²A)

→ (5 - 2 × ¼)/(1 - 2 × ¼)

→ (5 - ½)/(1 - ½)

→ 9/2 × 2

→ 9

Hence final answer is 9.