Question

[Linh Linh]

1)Rút gọn

B= \(\sqrt{sin^2x\left(1+cotx\right)+cos^2x\left(1+tanx\right)}\)

2)Tính giá trị biểu thức

A=\(\dfrac{2sina+cosa}{cosa-3sina}\)nếu tan a=-2

Answer 1

[Nguyen]

\(\dfrac{1}{\cos^2x}=1+\tan^2x=1+4=5\)\(\Rightarrow\cos^2x=\dfrac{1}{5}\Rightarrow\cos x=\dfrac{\sqrt{5}}{5}\)\(\Rightarrow\sin x=\tan x.\cos x=\left(-2\right).\dfrac{\sqrt{5}}{5}=\dfrac{-2\sqrt{5}}{5}\)

\(A=\dfrac{\dfrac{-4\sqrt{5}}{5}+\dfrac{\sqrt{5}}{5}}{\dfrac{\sqrt{5}}{5}+\dfrac{6\sqrt{5}}{5}}\)\(=\dfrac{-3}{7}\)