Question

If 7cos^2 A +3sin^2 A = 4 find value of TanA

Answer 1

3sin²A + 7cos²A = 4

=3sin²A + 3cos²A + 4cos²A = 4

=4cos²A + 3(sin²A + cos²A) = 4  --------(sin²A + cos²A =1)

=4cos²A + 3 = 4

=4cos²A = 4 – 3 = 1

=cos²A = 1/4

=cosA = √1/4

=cosA = 1/2

=cosA =cos60  (cos60 = 1/2)

=A = 60

Therefore tanA = √3  (tan60 = √3)