Question

Find the value of tanA if 7sin²A+3cos²A=4

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 30°=1/√3
$= \huge \bold{\frac{1}{ \sqrt{3} } }$