# How do you prove (sinx+cosx)/(secx+cscx)=sinx/secx?

Aug 25, 2016

See below.

#### Explanation:

Apply the following identities:

$\sec \theta = \frac{1}{\cos} \theta$

$\csc \theta = \frac{1}{\sin} \theta$

Now, simplify both sides using the given identities:

$\frac{\sin x + \cos x}{\frac{1}{\cos} x + \frac{1}{\sin} x} = \sin \frac{x}{\frac{1}{\cos} x}$

$\frac{\sin x + \cos x}{\frac{\sin x + \cos x}{\sin x \cos x}} = \sin x \cos x$

$\sin x + \cos x \times \frac{\sin x \cos x}{\sin x + \cos x} = \sin x \cos x$

$\cancel{\sin x + \cos x} \times \frac{\sin x \cos x}{\cancel{\sin x + \cos x}} = \sin x \cos x$

$\sin x \cos x = \sin x \cos x$

Identity proved!!

Hopefully this helps!