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b: \(B=\left(1+\cos\alpha\right)\left(1-\cos\alpha\right)-\sin^2\alpha\)
\(=1-\cos^2\alpha-\sin^2\alpha\)
=0
\(A=sin^4a+2\cdot sin^4a\cdot cos^2a+cos^4a+2\cdot cos^4a\cdot sin^2a\)
\(=\left(sin^4a+cos^4a\right)+2\cdot sina^2a\cdot cos^2a\left(sin^2a+cos^2a\right)\)
\(=sin^4a+cos^4a+2\cdot sin^2a\cdot cos^2a\)
\(=\left(sin^2a+cos^2a\right)^2=1\)
a/ \(A=\left(sin\alpha+cos\alpha\right)^2+\left(sin\alpha-cos\alpha\right)^2=2\left(sin^2\alpha+cos^2\alpha\right)=2\)
b/ \(B=\left(1+tan^2\alpha\right)\left(1-sin^2\alpha\right)-\left(1+cotg^2\alpha\right)\left(1-cos^2\alpha\right)\)
\(=\left(1+\frac{sin^2\alpha}{cos^2\alpha}\right)\left(1-sin^2\alpha\right)-\left(1+\frac{cos^2\alpha}{sin^2\alpha}\right)\left(1-cos^2\alpha\right)\)
\(=\frac{1}{cos^2\alpha}.cos^2\alpha-\frac{1}{sin^2\alpha}.sin^2\alpha=1-1=0\)
b) tan 2 α - sin 2 α . tan 2 α
= tan 2 α (1 - sin 2 α )
= tan 2 α . cos 2 α
= sin 2 α
