Simplifying the Trigonometric Expression Question

[Deaddman]

Homework Statement

cosx/(secx+tanx)

The Attempt at a Solution

So far I have this:

=cosx/(1/cosx + sinx/cosx)
=cosx/(sinx + 1/cosx)
=cos²x/sinx + 1

From there I don't know what to do. I've messed around with it for a while but don't seem to get anywhere.

Any help is appreciated.

 

[Russell Berty]

Your last denominator is incorrect. It should be sinx + 1.

 

[Deaddman]

Yeah you're right, thanks for pointing it out. Fixed now.

 

[yeongil]

cos² x/(1 + sin x)
(Let's keep the order of 1 and sin x.)

Here's a hint: do you know of an identity that has a sin x (or a multiple or a power thereof) and a cos x (as before) in it?


01

 

[Deaddman]

Ahhh, I think I got it.

1-sin² x/1+sin x

(1-sin x)(1+sin x)/1+sin x

1-sin x!

Right?

 

[yeongil]

Indeed that is correct!01