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

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

Answers (1)

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

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