Question

a) \(\sin\alpha.\cos\alpha.\left(\tan\alpha+\cot\alpha\right)\)

b)\(\cot^2-\cos^2.\cot^2\)

c)\(\tan^2-\sin^2.\tan^2\)

Đơn giản các biểu thức trên

Answer 1

Mình thay \(\alpha\) thành x để tiện ghi nhé

a) \(sinx.cosx\left(tanx+cotx\right)\)

\(=sinx.cosx\left(\dfrac{sinx}{cosx}+\dfrac{cosx}{sinx}\right)\)

\(=sinx.cosx\left(\dfrac{sinx^2+cosx^2}{sinx.cosx}\right)\)

\(=\dfrac{sinx.cosx}{sinx.cosx}=1\)

b) \(cot^2-cos^2.cot^2\)

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

\(=\dfrac{cos^2-cos^2+sin^2cos^2}{sin^2}\)

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

\(=cos^2\)

c) \(tan^2-sin^2.tan^2\)

\(=tan^2\left(1-sin^2\right)\)

\(=\dfrac{sin^2}{cos^2}cos^2\)

\(=sin^2\)