Question

Verify the identity.

Answer 1

\[\frac{ 1-sinx }{ cosx }= \frac{ cosx }{ 1+sinx }\]

Answer 2

There are 3 ways to verify any identity...
1-start with the left and work your way to the right;
2-start with the right and work your way to the left;
3-start with the left and right and work your way to a common expression.

I'd like to work from left side to the right side here... ok?

Answer 3

ok

Answer 4

starting from the left side,
\(\large \frac{1-sinx}{cosx}= \frac{1-sinx}{cosx}\cdot \frac{1+sinx}{1+sinx}=\frac{1-sin^2x}{cosx \cdot (1+sinx)} \)
i'll stop here because you can probably simplify the numerator.....

Answer 5

u understand what happened here? can u simplify to get the right side of the identity?

Answer 6

the numerator should be 1-cos2x/2 rite?

Answer 7

no...
\(\large 1-sin^2x = cos^2x \)
so
\(\large \frac{1-sin^2x}{cosx(1+sinx)}=\frac{cos^{\cancel2}x}{\cancel{cosx}(1+sinx)}=\frac{cosx}{1+sinx} \)

Answer 8

oooooo. ok i c now. thank tou so much.

Answer 9

yw... :)