Question

Bài 10: Chứng minh rằng: tan²x - sin²x . tan²x=sin²x

lm hộ giúp mk ik mn ạ

Answer 1

Ta có : \(\tan\left(x\right)=\frac{\sin\left(x\right)}{\cos\left(x\right)}\)

\(\Leftrightarrow\tan^2\left(x\right)=\left(\frac{\sin\left(x\right)}{\cos\left(x\right)}\right)^2\)

\(\Leftrightarrow\tan^2\left(x\right)=\frac{sin^2\left(x\right)}{\cos^2\left(x\right)}\)

Và ta có : \(\cos^2\left(x\right)+\sin^2\left(x\right)=1\)

\(\Leftrightarrow\cos^2\left(x\right)=1-\sin^2\left(x\right)\)

VT: \(\tan^2\left(x\right)-\sin^2\left(x\right)\cdot\tan^2\left(x\right)\)

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

\(=\frac{\sin^2\left(x\right)}{\cos^2\left(x\right)}\cdot\cos^2\left(x\right)\)

\(=\sin^2\left(x\right)=VP\)(đpcm)

(chúc bạn học tốt)