Amber D.

asked • 04/07/21

Use identities to rewrite cosx+sinxtanx in terms of sin x and cos x. Then simplify so that no quotients appear.

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Doug C. answered • 04/07/21

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cosx + sinx(sinx/cosx) ; replace tanx with sinx / cosx (quotient identity)


cos2x/cosx + sin2x/cosx ; get a common denominator my multiplying first term by cosx/cosx


(cos2x + sin2x) / cosx (place the sum of the numerators over the common denominator)


1/cosx (use they Pythagorean identity sin2x + cos2x = 1)


Finally:


secx ; use the reciprocal identity 1/cos x = sec x


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Amber D.

how did you get 1/cosx using that identity??? am I figuring out what square root of sin and cos are?
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04/07/21

Doug C.

Hopefully the short video makes it clear. There already is a cos x in the denominator of the fraction. Use the Pythagorean identity to replace the complicated looking numerator with a 1. Then use the reciprocal identity.
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04/07/21

Amber D.

sorry im late responding , the video did make it super clear. you're a life saver!
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04/09/21

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