# verify that (sinθ+tanθ)/(1+cosθ)=tanθ

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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`

mun55 | Student, Grade 10 | (Level 2) eNoter

Posted on

The identity  has to be verified.

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This proves:

mun55 | Student, Grade 10 | (Level 2) eNoter

Posted on

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

lochana2500 | Student, Undergraduate | (Level 1) Valedictorian

Posted on

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