Question

A simplificação da expressão (2 cos⁡x-sen x∙(cotg x-tg x) )∙cos⁡x vale?

Answer 1

$(2 \cos x-\sin x\cdot(\cot x-\tan x) )\cdot\cos x=\\\\\left(2\cos x-\sin x\left(\dfrac{\cos x}{\sin x}-\dfrac{\sin x}{\cos x}\right)\right)\cos x=\\\\\\\left(2\cos x-\sin x\left(\dfrac{\cos^2 x}{\sin x\cos x}-\dfrac{\sin^2 x}{\sin x\cos x}\right)\right)\cos x=\\\\\\\left(2\cos x-\left(\dfrac{\cos^2 x-\sin^2 x}{\cos x}\right)\right)\cos x=\\\\\\\left(\dfrac{2\cos^2 x}{\cos x}-\left(\dfrac{\cos^2 x-\sin^2 x}{\cos x}\right)\right)\cos x=\\\\\\\left(\dfrac{\cos^2 x+\sin^2x}{\cos x}\right)\cos x=1$