Question

If 3 tan A =4, then value of √1-sin A/1+cos A is

Answer 1

3tanA = 4

tanA = 4/3 = perpendicular/base

so, perpendicular = 4
and base = 3
from Pythagoras theorem,
hypotenuse = √(3² + 4²) = 5

now , sinA = perpendicular/hypotenuse = 4/5
cosA = base/hypotenuse = 3/5

so, $\sqrt{\frac{1-sinA}{1+cosA}}$

= $\sqrt{\frac{1-\frac{4}{5}}{1+\frac{3}{5}}}$

= $\sqrt{\frac{1}{8}}$

= $\frac{1}{2\sqrt{2}}$

Answer 2

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.