Question

Rút gọn:

A= \(\sin^6\alpha+cos^6\alpha+3sin^2\alpha.cos^2\alpha\)

B= \(\left(cos\alpha-sin\alpha\right)^2+\left(cos\alpha+sin\alpha\right)^2\)

C= \(\dfrac{\left(cos\alpha-sin\alpha\right)^2-\left(cos\alpha+sin\alpha\right)^2}{sin\alpha.cos\alpha}\)

Answer 1

Lời giải:
\(A=(\sin ^2a)^3+(\cos ^2a)^3+3\sin ^2a\cos ^2a(\sin ^2a+\cos ^2a)\)

\(=(\sin ^2a+\cos ^2a)^3=1^3=1\)

\(B=(\cos ^2a+\sin ^2a-2\sin a\cos a)+(\cos ^2a+\sin ^2a+2\sin a\cos a)\)

\(=(1-2\sin a\cos a)+(1+2\sin a\cos a)=2\)

\(C=\frac{(\cos ^2a+\sin ^2a-2\sin a\cos a)-(\cos ^2a+\sin ^2a+2\sin a\cos a)}{\sin a\cos a}=\frac{(1-2\sin a\cos a)-(1+2\sin a\cos a)}{\sin a\cos a}\)

$=\frac{-4\sin a\cos a}{\sin a\cos a}=-4$