Question

If 7sin^2 A + cos^2 A = 4, then show that tan A is

Answer 1

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 !!