# verify???

• March 5th 2008, 03:49 PM
iheartthemusic29
verify???
(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!
• March 5th 2008, 04:25 PM
Mathnasium
On the left, replacing everything with sine and cosine, gives:

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

Getting common denominators in both the numerator and the denominator:

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

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

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

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