Question

If tan0=20/21show that(1-sin0+cos0)/(1+sin0+cos0)=3/7

Answer 1

Tan theta = opposite side/ efficient side= 20/21

Let x be the hypotenuse By applying Pythagoras we get,

AC²+BC²+AB²

x²= (20)²+(21)²

x²= 400+ 441

x²=841

x=29

Sin theta = AB/AC= 20/29

Cos theta = BC/AC= 21/29

SUBSTITUTE:- Sin theta snd Cos theta in equation

we get,

1-sin theta+cos theta÷1+sin theta+ cos theta

=1-20/29+21/29 ÷ 1+20/29+21/29

=(29-20+21)/29 ÷ (29+20+21)/29

=30/29÷70/29

=30/29×29/70

=3/7