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“Find the trig identity” I’m in need of help on number 3

“Find the trig identity” I’m in need of help on number 3-example-1
User Jawsware
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1 Answer

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SOLUTION

(3) We want to prove the trig identity


(sin(x)+sin(x).cot^2(x))/(csc(x))=1

This becomes


\begin{gathered} (sin(x)+sin(x).cot^2(x))/(csc(x))=1 \\ (sin(x)+(sin(x)*(1)/(tan^2(x))))/((1)/(sin(x))) \\ (sin(x)+(sin(x)*(cos^2(x))/(sin^2(x))))/((1)/(sin(x))) \\ (sin(x)+(cos^2(x))/(sin(x)))/((1)/(sin(x))) \end{gathered}

Changing the division to multiplication for thedenominator, we have


\begin{gathered} (sin(x)+(cos^2(x))/(sin(x)))* sin(x) \\ =sin^2(x)+cos^2(x) \\ =1 \end{gathered}

User Chris Midgley
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