Question

[Hà Nguyễn]

1/Rút gọn :

\(G=\left(1-sin^2x\right)cot^2x+1-cot^2x\)

2/ Nếu \(tan\alpha+cot\alpha=2\) thì \(tan^2\alpha+cot^2\alpha\) bằng bao nhiêu? 

Answer 1

[Nguyễn Việt Lâm]

\(G=cot^2x-sin^2x.cot^2x+1-cot^2x=1-sin^2x.cot^2x\)

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

2.

\(tana+cota=2\Rightarrow\left(tana+cota\right)^2=4\)

\(\Rightarrow tan^2a+cot^2a+2tana.cota=4\)

\(\Rightarrow tan^2a+cot^2a+2=4\)

\(\Rightarrow tan^2a+cot^2a=2\)