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for sin(angle)+cos(angle)cot(angle)=csc(angle)-- prove the equation algebraically? 

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ssdixon | Student, Undergraduate | (Level 1) Salutatorian

Posted May 6, 2012 at 5:22 AM via web

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for sin(angle)+cos(angle)cot(angle)=csc(angle)-- prove the equation algebraically? 

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zororro | Student, Undergraduate | eNotes Newbie

Posted May 6, 2012 at 5:29 AM (Answer #1)

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sin+cos(cos/sin)

Common denominatior is sin so it becomes:

(sin^2+cos^2)/(sin)

We know that sin^2+cos^2 = 1 so on we get:

1/sin

Which is equal to csc of theta.

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beckden | High School Teacher | (Level 1) Educator

Posted May 6, 2012 at 5:31 AM (Answer #2)

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`cot(theta)=(cos(theta))/(sin(theta))` and

`sin^2(theta)+cos^2(theta) = 1`   so

`sin(theta)+cos(theta)cot(theta) =`

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

`(sin^2(theta))/(sin(theta))+(cos^2(theta))/(sin(theta)) =`

`(sin^2(theta)+cos^2(theta))/(sin(theta)) =`

`1/sin(theta) = csc(theta)`

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