(secx+cscx)/(1+tanx)=cscx

I put the entire thing in terms of sine and cosine, but I keep getting stuck. Please and thank you!

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- Mar 5th 2008, 03:49 PMiheartthemusic29verify???
(secx+cscx)/(1+tanx)=cscx

I put the entire thing in terms of sine and cosine, but I keep getting stuck. Please and thank you! - Mar 5th 2008, 04:25 PMMathnasium
On the left, replacing everything with sine and cosine, gives:

$\displaystyle \frac {\frac{1}{cos x} + \frac{1}{sin x}}{1 + \frac {sin x}{cos x}}$

Getting common denominators in both the numerator and the denominator:

$\displaystyle \frac {\frac {sin x + cos x}{sin x cos x}}{\frac {sin x + cos x}{cos x}}$

Remember that dividing by a fraction is the same as multiplying by the reciprocal:

$\displaystyle \frac {sin x + cos x}{sin x cos x} \times \frac {cos x}{sin x + cos x}$.

The $\displaystyle sin x + cos x$ should cancel, as does a single $\displaystyle cos x$ and voila!