MHB Prove identity (sinx+cosx)/(secx+cscx)= sinxcosx

[guinessvolley]

prove this identity

(sinx+cosx)/(secx+cscx)= sinxcosx if you could list out the steps it would be appreciated

 

[MarkFL]

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:

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

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