Question

It 7 sin²A+ 3 cos²A=4& A is acute angle,
then the value of tan2A = ?​

Answer 1

Step-by-step explanation:

7sin²A + 3cos²A = 4

7(1 - cos²A) + 3cos²A = 4

7 - 7cos²A + 3cos²A = 4

7 - 4cos²A = 4

4cos²A = 7 - 4 = 3

cos²A = 3/4

cosA = √3/2

We know that, cos 30° = √3/2

A = 30°

tan2A = tan(2 × 30°) = tan60° = √3