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Please zoom in your screen if you're having trouble reading small texts. The following equations will look small.

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:

Factor sinx from the numerator,

Cancel cosx+1,


Hope that helps. 
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