# Solve frac{csc x(sin^{2}x+cos^{2}xtan x)}{sin x+cos x}

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

2020-11-11
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
$$=\frac{\sin x+\cos x}{\sin x+\cos x}=1$$

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