# Trigonometryprove identity (sinx+cosx)/(secx+cscx)= sinxcosx

#### guinessvolley

##### New member
prove this identity

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

if you could list out the steps it would be appreciated

#### MarkFL

##### Pessimist Singularitarian
Staff member
Hello, and welcome to MHB!

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?