3 years ago

PLEASE I JUS NEED HELP PLEASE

Mathematics

1 answer:

nika2105 [10]3 years ago

4 0

Answer:

I am sorry

Step-by-step explanation:

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

stealth61 [152]

<h3>Answer: Choice E) 1</h3>

Work Shown:

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

Therefore, $\frac{(1-\sin(\beta))(1+\sin(\beta))}{\cos^2(\beta)}=1\\\\$ is an identity for all values of β for which the original expression is defined. I used the difference of squares rule for the 2nd step. Then I applied the pythagorean trig identity for the 3rd step.