Question

Hãy đơn giản các biểu thức sau:

a) \(\sin^4\alpha+\cos^4\alpha+2\sin^2\alpha.\cos^2\alpha\)

b) \(\tan^2\alpha\left(2.\cos^2\alpha+\sin^2\alpha-1\right)\)

Answer 1

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

Answer 2

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