Question

If 1 + sin^2 A = 3 sinA cosA the prove that tan A = 1 or 1/2

Answer 1

Hello friend ..

This question had come in this year's maths board paper..

1+Sin²A= 3SinA Cos A.

Cos²A+Sin²A+Sin²A = 3SinA CosA [ 1 = Sin²+Cos A]

Cos²A+2Sin²A = 3SinA CosA....(1)

DIVIDE (1) BY COS²A we get,

1+2Tan²A = 3 TanA

1+2Tan²A - 3 TanA = 0

(2TanA-1) ( TanA-1) = 0

2TanA -1 = 0. TanA -1= 0

2TanA = 1. TanA =1

TanA = 1/2. TanA = 1

Hope it helps..☆☆♡☆☆