# How do you prove (secx+tanx)((1-sinx)/cosx)=1?

Jun 26, 2018

As proved below.

#### Explanation:

We will use some of the above identities to prove the sum.

$\text{To prove } \left(\sec x = \tan x\right) \left(\frac{1 - \sin x}{\cos} x\right) = 1$

$L H S = \left(\frac{1}{\cos} x + \sin \frac{x}{\cos} x\right) \left(\frac{1 - \sin x}{\cos} x\right)$

$\implies \frac{\left(1 + \sin x\right) \left(1 - \sin x\right)}{\cos} ^ 2 x$

$\implies \frac{1 - {\sin}^{2} x}{1 - {\sin}^{2} x} = 1 = R H S$