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EleoNora [17]
2 years ago
6

Which expression is equivalent to (1−sinβ)(1+sinβ)/cos2β for all values of β for which (1−sinβ)(1+sinβ)/cos2β is defined?

Mathematics
1 answer:
Effectus [21]2 years ago
7 0

Using a trigonometric identity, it is found that the equivalent expression is given by 1.

<h3>What are the trigonometric identities used to solve this question?</h3>

Relating sine and cosine, we have that:

\sin^{2}{\beta} + \cos^{2}{\beta} = 1

Then:

\cos^{2}{\beta} = 1 - \sin^{2}{\beta}

For the tangent, we have that:

\tan{\beta} = \frac{\sin{\beta}}{\cos{\beta}}.

For the secant, we have that:

\sec{\beta} = \frac{1}{\cos{\beta}}.

In this problem, the expression is:

\frac{(1 - \sin{\beta})(1 + \sin{\beta})}{\cos^{2}{\beta}} = \frac{1 - \sin^2{\beta}}{\cos^2{\beta}} = \frac{\cos^2{\beta}}{\cos^2{\beta}} = 1

More can be learned about trigonometric identities at brainly.com/question/7331447

#SPJ1

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