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# Prove a trig identity

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Hi.

Thank you so much in advance.

I need help proving

\(csc(x)/(cot(x)+tan(x)) = cos(x)\)

bqrs01  Aug 30, 2017
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### 1+0 Answers

#1
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csc x / [ cot x + tanx ]  =   write in terms of sine and cosine

[ 1 / sin x] / [( cos x / sinx) + (sin x / cos x) ]      get a common denominator on the bottom

[ 1 / sinx] / ( [ cos^2 x +  sin^2 x ]  / [sin x cosx ] )  =

1                               [ cos^2 x +  sin^2 x ]

___         รท               ___________________       =

sin x                              sin x cosx

1                                    sin x cos x

___          X               ___________________   =        swap numerators

sin x                             [ cos^2 x +  sin^2 x ]

sin x cos x        X           1

_________                  ____     =

sin x                              1

cos x

CPhill  Aug 30, 2017

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