Question

[ngân nguyểnthị]

Giúp tớ vs:

Rút gọn biểu thức

\(P=\dfrac{\left(sinx+cosx\right)^2-1}{\tan x-\sin x.\cos x}\)

Answer 1

[Hung nguyen]

\(P=\dfrac{\left(\sin x+\cos x\right)^2-1}{\tan x-\sin x.\cos x}=\dfrac{\sin^2x+\cos^2x+2\sin x.\cos x-1}{\dfrac{\sin x}{\cos x}-\sin x.\cos x}\)

\(=\dfrac{2\sin x.\cos^2x}{\sin x.\left(1-\cos^2x\right)}=\dfrac{2\cos^2x}{\sin^2x}=2\tan^2x\)