## anonymous one year ago Verify the identity. quantity one minus sine of x divided by cosine of x equals cosine of x divided by quantity one plus sine of x

1. anonymous

looks like this $\frac{ 1 - sinx }{ cosx } = \frac{ cosx }{ 1 + sinx }$

2. Nnesha

cross multiply ?

3. Nnesha

or i would solve right to make it equal

4. Nnesha

right side*

5. anonymous

6. Nnesha

you need to multiply denominator and numerator by the conjugate of 1+sinx

7. anonymous

ahh ok

8. anonymous

so it is $\frac{ cosx - sinxcosx }{ 1-\sin^2x}$

9. Nnesha

okay so you don't need to distribute 1-sinx by cosx at the numerator $\frac{ \cos(x)(1-\sin(x)) }{ 1-\sin^2 }$ apply the identity 1-sin^2x equal to what ?

10. anonymous

cos^2x

11. anonymous

so it would be $\frac{ cosx(1-sinx) }{ \cos^2x }$

12. Nnesha

yes right cos^2x can be written as cos x times cos x $\huge\rm \frac{ \cos(x)(1-\sin(x)) }{ cos(x) \times cos(x) }$

13. anonymous

so factor out top and bottom leaves me with $\frac{ 1-sinx }{ cosx }$

14. Nnesha

yep

15. anonymous

and thats it

16. anonymous

ty!

17. Nnesha

yep

18. Nnesha

my pleasure!