Question

a) \(\cos^2\)α+ \(\cos^2\)β + \(\cos^2\)α.\(\sin^2\)β +\(^{ }\sin^2\)α

b) 2(\(\sin\)α - \(\cos\)α)\(^2\) - ( \(\left(\sin\alpha+\cos\alpha\right)^{2^{ }}+\left(\sin\alpha.\cos\alpha\right)\)

c) \(\left(\tan\alpha-\cot\alpha\right)^2-\left(\tan\alpha+\cos\alpha\right)^2\)

Answer 1

Lời giải:
a)

\(\cos ^2a+\cos ^2b+\cos ^2a\sin ^2b+\sin ^2a\)

\(=(\cos ^2a+\sin ^2a)+\cos ^2b+\cos ^2a\sin ^2b\)

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

\(=2-\sin ^2b(1-\cos ^2a)=2-\sin ^2b\sin ^2a\)

b)

\(2(\sin a-\cos a)^2-[(\sin a+\cos a)^2+\sin a\cos a]\)

\(=2(\sin ^2a-2\sin a\cos a+\cos ^2a)-[\sin ^2+2\sin a\cos a+\cos ^2a+\sin a\cos a]\)

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

\(=1-7\sin a\cos a\)

c)

\((\tan a-\cot a)^2-(\tan a+\cot a)^2\)

\(=\tan ^2a+\cot ^2a-2\tan a\cot a-(\tan ^2a+\cot ^2a+2\tan a\cot a)\)

\(=-4\tan a\cot a=-4\)