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verify that (sinθ+tanθ)/(1+cosθ)=tanθ

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renegade420 | Student, Undergraduate | eNotes Newbie

Posted April 26, 2012 at 1:14 AM via web

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verify that (sinθ+tanθ)/(1+cosθ)=tanθ

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted April 26, 2012 at 1:31 AM (Answer #1)

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The identity `(sin theta + tan theta)/(1 + cos theta) = tan theta` has to be verified.

`(sin theta + tan theta)/(1 + cos theta)`

=> `(sin theta + (sin theta)/(cos theta))/(1 + cos theta)`

=> `(sin theta*cos theta + sin theta)/(cos theta*(1 + cos theta))`

=> `(sin theta(1 + cos theta))/(cos theta*(1 + cos theta))`

=> `(sin theta)/(cos theta)`

=> `tan theta`

This proves: `(sin theta + tan theta)/(1 + cos theta) = tan theta`

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lochana2500 | TA , Undergraduate | Valedictorian

Posted July 5, 2012 at 3:21 PM (Answer #2)

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L:H:S: = (sinθ+tanθ)/(1+cosθ)

= (sinθ.cosθ+sinθ)/cosθ(1+cosθ)

= sinθ(cosθ+1)/cosθ(cosθ+1)

= sinθ/cosθ

= tanθ

= R:H:S

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mun55 | Student, Grade 10 | eNoter

Posted September 25, 2012 at 7:51 PM (Answer #4)

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L:H:S: = (sinθ+tanθ)/(1+cosθ)

= (sinθ.cosθ+sinθ)/cosθ(1+cosθ)

= sinθ(cosθ+1)/cosθ(cosθ+1)

= sinθ/cosθ

= tanθ

= R:H:S

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mun55 | Student, Grade 10 | eNoter

Posted September 25, 2012 at 7:52 PM (Answer #5)

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The identity  has to be verified.

=> 

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=> 

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This proves: 

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