Question

HOTS If 7 sin^2 A + 3 cos^2 A = 4, prove that

tan A=1/root3
​

Answer 1

Here is your answer !!

7 sin²A + 3 cos²A = 4

=> 3 sin²A + 3 cos²A + 4 sin²A = 4

=> 3 ( sin²A + cos²A ) + 4 sin²A = 4

=> 3 + 4 sin²A = 4

=> 4 sin²A = 1

=> sin²A = 1/4

=> sin A = 1/2

=> sin A = sin 30°

=> A = 30° .

So , tan A = tan 30° = 1/√3 _______ [Proved]

Hope it helps !!

Answer 2

Answer:

7sin²A+3cos²A=4

3sin²A+3cos²A=4-4sin²A

3=4(1-sin²A)

cos²A=3/4

cosA=√3/2

A=30°

tan30°=1/√3