Question #6b892

1 Answer
Sep 21, 2017

tanx=sinx/cosx so you can use identities to get to a point where the sin/cos parts can be written as tans.

Explanation:

(1-cscx)/(1-cscx)=1 so first of all it's just multiplying cosx/(1+cscx) by one.

Now to look at the first part:
write it as cosx/1*1/(1+cscx)

Then 1+cscx=1+1/sinx :. 1/(1+cscx) = (sinx)/(sinx+1)

Recombining with that cos(x) that I put aside:
(cosx*sinx)/(sinx+1)

sinx/(tanx+1) is the closest I can get.

I'm not quite sure why you say the answer should be tanx-tanxsinx. When I check with Wolfram http://www.wolframalpha.com/input/?i=(cosx%2F(1%2Bcscx)+ the answer isn't tanx-tanxsinx either. Are you sure that you've entered the question correctly?