Question

Probe that:
$\sec \alpha \sqrt{1 - \sin( {}^{2} ) } \alpha = 1$
​

Answer 1

Step-by-step explanation:

$\sec \alpha \sqrt{1 - \sin ^{2} \alpha } = 1$

Prove the LHS

Using trigonometric identities

That's

$\cos ^{2} \alpha = 1 - \sin^{2} \alpha$

Rewrite the expression

We have

$\sec \alpha \sqrt{ \cos^{2} \alpha }$

$\sqrt{ { \cos }^{2} \alpha } = \cos \alpha$

So we have

$\sec \alpha \times \cos \alpha$

Using trigonometric identities

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

Rewrite the expression

That's

$\frac{1}{\cos \alpha } \times \cos \alpha$

Reduce the expression with cos a

We have the final answer as

1

As proven

Hope this helps you