**3sin**^{2}A + 7cos^{2}A = 4

**=3sin**^{2}A + 3cos^{2}A + 4cos^{2}A = 4

**=4cos**^{2}A + 3(sin^{2}A + cos^{2}A) = 4 --------(sin^{2}A + cos^{2}A =1)

**=4cos**^{2}A + 3 = 4

**=4cos**^{2}A = 4 – 3 = 1

**=cos**^{2}A = 1/4

**=cosA = √1/4**

**=cosA = 1/2**

**=cosA =cos60 (cos60 = 1/2)**

**=A = 60**

**Therefore tanA = √3 (tan60 = √3)**