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


New member
May 15, 2019
prove this identity

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

if you could list out the steps it would be appreciated


Pessimist Singularitarian
Staff member
Feb 24, 2012
St. Augustine, FL.
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?