(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!
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!