Question

if 3 tan A = 4 , find the value of (1+sin A) / (1+cosA)

Answer 1

Step-by-step explanation:

3 Tan A = 4

Tan A = 4/3 = P / B

Perpendicular = 4 and Base = 3.

By Pythagoras theroem ,

( Hypotenuse )² = ( Perpendicular)² + ( Base)²

( H )² = (4)² + (3)²

( H )² = 16 + 9

H = √25 = 5

Therefore,

Sin A = Perpendicular / Hypotenuse = 4/5

And,

Cos A = Base / Hypotenuse = 3/5

Therefore,

√ 1 - SinA / 1 + CosA = √ 1 - 4/5 / 1 + 3/5

=> √5-4/5 / 5 + 3 / 5

=> √1/5 / 8 / 5

=> √ 1/5 × 5/8

=> √1/8

=> √1/2×2×2

=> √1/2√2.