Answer
$\dfrac{\cos x}{\sec x}+\dfrac{\sin x}{\csc x}=1$
Work Step by Step
$\dfrac{\cos x}{\sec x}+\dfrac{\sin x}{\csc x}=1$
Substitute $\sec x$ with $\dfrac{1}{\cos x}$ and $\csc x$ with $\dfrac{1}{\sin x}$ and simplify:
$\dfrac{\cos x}{\Big(\dfrac{1}{\cos x}\Big)}+\dfrac{\sin x}{\Big(\dfrac{1}{\sin x}\Big)}=1$
$\cos^{2}x+\sin^{2}x=1$
Since $\cos^{2}x+\sin^{2}x=1$, the identity is proved:
$1=1$
