Answer
$\dfrac{\sin x+\cos x}{\sec x+\csc x}=\sin x\cos x$
Work Step by Step
$\dfrac{\sin x+\cos x}{\sec x+\csc x}=\sin x\cos x$
On the left side of the equation, replace $\sec x$ by $\dfrac{1}{\cos x}$ and $\csc x$ by $\dfrac{1}{\sin x}$:
$\dfrac{\sin x+\cos x}{\dfrac{1}{\cos x}+\dfrac{1}{\sin x}}=\sin x\cos x$
Evaluate $\dfrac{1}{\cos x}+\dfrac{1}{\sin x}$:
$\dfrac{\sin x+\cos x}{\dfrac{\sin x+\cos x}{\sin x\cos x}}=\sin x\cos x$
Evaluate the division and the identity will be proved:
$\dfrac{\sin x\cos x(\sin x+\cos x)}{\sin x+\cos x}=\sin x\cos x$
$\sin x\cos x=\sin x\cos x$
