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Trigonometry prove identity (sinx+cosx)/(secx+cscx)= sinxcosx

guinessvolley

New member
May 15, 2019
1
prove this identity

(sinx+cosx)/(secx+cscx)= sinxcosx


if you could list out the steps it would be appreciated
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,735
Hello, and welcome to MHB! (Wave)

Since the RHS is in terms of the sine and cosine functions, the first thing I would do is write the LHS in terms of these functions only:

\(\displaystyle \frac{\sin(x)+\cos(x)}{\dfrac{1}{\cos(x)}+\dfrac{1}{\sin(x)}}\)

Now, combine terms in the denominator...what do you get?