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Airida [17]
3 years ago
12

Probe that:

29%20%7D%20%20%5Calpha%20%20%3D%201" id="TexFormula1" title=" \sec \alpha \sqrt{1 - \sin( {}^{2} ) } \alpha = 1" alt=" \sec \alpha \sqrt{1 - \sin( {}^{2} ) } \alpha = 1" align="absmiddle" class="latex-formula">
​
Mathematics
1 answer:
Nataly [62]3 years ago
7 0

Step-by-step explanation:

<h3>\sec \alpha  \sqrt{1 -  \sin ^{2}   \alpha }  = 1</h3>

Prove the LHS

Using trigonometric identities

That's

<h3>\cos ^{2}  \alpha  = 1 -  \sin^{2}  \alpha</h3>

<u>Rewrite the expression</u>

We have

<h3>\sec \alpha  \sqrt{ \cos^{2} \alpha  }</h3>

<h3>\sqrt{ { \cos }^{2}  \alpha }  =  \cos \alpha</h3>

So we have

<h3>\sec  \alpha  \times  \cos \alpha</h3>

Using trigonometric identities

<h3>\sec \alpha  =  \frac{1}{ \cos \alpha }</h3>

<u>Rewrite the expression</u>

That's

<h3>\frac{1}{\cos \alpha }  \times  \cos \alpha</h3>

Reduce the expression with cos a

We have the final answer as

<h2>1</h2>

As proven

Hope this helps you

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