Question

Solve \(\frac{\csc x(sin^{2}x+cos^{2}x\tan x)}{\sin x+\cos x}\)

Answer 1

Write in terms of sine and cosine:
\(=\frac{(\frac{1}{\sin x})(sin^{2}x+cos^{2}x\times\frac{\sin x}{\cos x})}{(\sin x+\cos x)}\)
Simplify:
\(\frac{(1/\sin x)(sin^{2}x+\cos x\sin x))}{(\sin x+\cos x)}\)
Apply distributive property: a(b+c)=ab+c
\(=\frac{\sin x+\cos x}{\sin x+\cos x}=1\)