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

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To prove the identity (sinx + cosx)/(secx + cscx) = sinx cosx, start by rewriting the left-hand side in terms of sine and cosine functions. The expression becomes (sinx + cosx)/(1/cosx + 1/sinx). Next, combine the terms in the denominator to simplify the expression further. This approach leads to a clearer path for demonstrating the equality with the right-hand side. The proof ultimately hinges on manipulating the trigonometric identities effectively.
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prove this identity

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

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