Answers

2014-04-03T07:12:54+08:00
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The equation is this:
 \frac{sinx+ tanx }{1+secx } =sinx

Recall these identities:
tanx= \frac{sinx}{cosx}
 secx= \frac{1}{cosx}

Doing the necessary substitution, we get:
 \frac{sinx+ \frac{sinx}{cosx} }{1+ \frac{1}{cosx} } =sinx

Combining, we will have:
( \frac{sinxcosx+sinx}{cosx}) /( \frac{cosx+1}{cosx})=sinx

When we divide, we multiply the numerator by the reciprocal of the denominator, we get:
 \frac{sinxcosx+sinx}{cosx}* \frac{cosx}{cosx+1}=sinx

We cancel cosx, then we get:
 \frac{sinxcosx+sinx}{cosx+1}=sinx

Factor sinx from the numerator,
 \frac{sinx(cosx+1)}{cosx+1}=sinx

Cancel cosx+1,
sinx=sinx

Yay.

Hope that helps. 
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