Question

[nguyễn minh hà]

*Rút gọn các biểu thức sau:

a/ sin⁴\(\alpha\)+ cos⁴\(\alpha\)+2sin²\(\alpha\) \(\cos\)²\(\alpha\)

b/ tan²\(\alpha\) - sin² \(\alpha\) tan²\(\alpha\)

c/ cos²\(\alpha\) + tan²\(\alpha\) cos² \(\alpha\)

ĐS: a/1

       b/sin²\(\alpha\)

      c/ 1

giúp với, gấp lắm!!!

Answer 1

[Hoàng Lê Bảo Ngọc]

a/\(sin^4\alpha+cos^4\alpha+2sin^2\alpha.cos^2\alpha=\left(sin^2\alpha+cos^2\alpha\right)^2=1\)

b/ \(tan^2\alpha-sin^2\alpha.tan^2\alpha=tan^2\alpha\left(1-sin^2\alpha\right)=\frac{sin^2\alpha}{cos^2\alpha}.cos^2\alpha=sin^2\alpha\)

c/ \(cos^2\alpha+tan^2\alpha.cos^2\alpha=cos^2\alpha\left(1+tan^2\alpha\right)\)

\(=cos^2\alpha.\left(1+\frac{sin^2\alpha}{cos^2\alpha}\right)=cos^2\alpha.\left(\frac{sin^2\alpha+cos^2\alpha}{cos^2\alpha}\right)\)

\(=cos^2.\frac{1}{cos^2\alpha}=1\)