Bài 29:
a: \(cos^2\alpha\cdot cos^2\beta+cos^2\alpha\cdot\sin^2\beta+\sin^2\alpha\)
\(=cos^2\alpha\left(\sin^2\beta+cos^2\beta\right)+\sin^2\alpha\)
\(=cos^2\alpha+\sin^2\alpha\)
=1
b: \(2\cdot\left(\sin\alpha-cos\alpha\right)^2-\left(\sin\alpha+cos\alpha\right)^2+6\cdot\sin\alpha\cdot cos\alpha\)
\(=2\cdot\left(1-2\cdot\sin\alpha\cdot cos\alpha\right)-\left(1+2\cdot\sin\alpha\cdot cos\alpha\right)+6\cdot\sin\alpha\cdot cos\alpha\)
\(=2-4\cdot\sin\alpha\cdot cos\alpha-1-2\cdot\sin\alpha\cdot cos\alpha+6\cdot\sin\alpha\cdot cos\alpha\)
=2-1
=1
c: \(\left(\tan\alpha-\cot\alpha\right)^2-\left(\tan\alpha+\cot\alpha\right)^2\)
\(=\left(\tan\alpha-\cot\alpha-\tan\alpha-\cot\alpha\right)\left(\tan\alpha-\cot\alpha+\tan\alpha+\cot\alpha\right)\)
\(=-2\cdot\cot\alpha\cdot2\cdot\tan\alpha=-4\)
Bài 27:
a: \(cos^4\alpha-\sin^4\alpha\)
\(=\left(cos^2\alpha-\sin^2\alpha\right)\left(cos^2\alpha+\sin^2\alpha\right)\)
\(=cos^2\alpha-\sin^2\alpha\)
b: \(\sin^4\alpha+cos^2\alpha\cdot\sin^2\alpha+\sin^2\alpha\)
\(=\sin^2\alpha\left(\sin^2\alpha+cos^2\alpha\right)+\sin^2\alpha\)
\(=\sin^2\alpha+\sin^2\alpha=2\cdot\sin^2\alpha\)
