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Can anyone help me verify the following trig identity:

$(1-\cos A)(1+\sec A)(\cot A)= \sin A.$

My work so far is

$(1-\cos A)\left(1+\frac{1}{\cos A}\right)\frac{\cos A}{\sin A}=\sin A$

But I am stuck around this part.

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    yes I meant sec=1/cos I just wrote my work part wrong.2012-07-14

1 Answers 1

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Express everything on the left in terms of sines and cosines. We get $(1-\cos A) \left(1+\frac{1}{\cos A}\right)\frac{\cos A}{\sin A}.$

First multiply $1+\frac{1}{\cos A}$ by the $\cos A$ in $\frac{\cos A}{\sin A}$. We get $\cos A+1$.Our expression is now equal to $(1-\cos A)(\cos A+1)\frac{1}{\sin A}.$ But $(1-\cos A)(\cos A+1)=(1-\cos A)(1+\cos A)=1-\cos ^2 A=\sin^2 A$. Now multiply by the $\frac{1}{\sin A}$. We get $\sin A$.

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    @Rakishi: You are welcome. As you can see, it is a minor slip that prevented you from pushing the argument through.2012-07-14