Question

I got stuck
Reduce to a trig. function:
(tanx+cotx)sinx

Answer 1

2cssec x

Answer 2

sry 2sec x

Answer 3

distribute; quotient identity twice\[=\frac{\sin^2x}{\cos x}+\frac{\cos x \sin x}{\sin x}\]common denominator\[=\frac{\sin^3x+\cos^2x \sin x}{\cos x \sin x}\]factor out sin x in numerator and cancel with sin x in denominator\[=\frac{\sin^2x + \cos^2x}{\cos x}\]Pythagorean identity\[=\frac{1}{\cos x}\]reciprocal identity\[=\sec x\]

Answer 4

From Mathematica:\[\text{TrigFactor}[\text{ }\text{ Sin}[x] (\text{ Cot}[x]+\text{Tan}[x])\text{ }]=\text{Sec}[x] \]