b: \(B=\sin^6a+cos^6a+3\cdot\sin^2a\cdot cos^2a\)
\(=\left(\sin^2a+cos^2a\right)^3-3\cdot\sin^2a\cdot cos^2a\cdot\left(\sin^2a+cos^2a\right)+3\cdot\sin^2a\cdot cos^2a\)
\(=1^3-3\cdot\sin^2a\cdot cos^2a+3\cdot\sin^2a\cdot cos^2a\)
=1
c: \(C=\sin^4a\left(1+2\cdot cos^2a\right)+cos^4a\left(1+2\cdot\sin^2a\right)\)
\(=\sin^4a+cos^4a+2\cdot\sin^4a\cdot cos^2a+2\cdot\sin^2a\cdot cos^4a\)
\(=\left(\sin^2a+cos^2a\right)^2-2\cdot sin^2a\cdot cos^2a+2\cdot\sin^2a\cdot cos^2a\left(\sin^2a+cos^2a\right)\)
\(=1-2\cdot\sin^2a\cdot cos^2a+2\cdot\sin^2a\cdot cos^2a=1\)
d: \(D=\sin^4a\left(3-2\cdot\sin^2a\right)+cos^4a\left(3-2\cdot cos^2a\right)\)
\(=3\cdot\left(\sin^4a+cos^4a\right)-2\cdot\sin^4a\cdot\sin^2a-2\cdot cos^2a\cdot cos^4a\)
\(=3\left\lbrack\left(\sin^2a+cos^2a\right)^2-2\cdot\sin^2a\cdot cos^2a\right\rbrack-2\cdot\left(\sin^6a+cos^6a\right)\)
\(=3\cdot\left\lbrack1-2\cdot\sin^2a\cdot cos^2a\right\rbrack-2\cdot\left\lbrack\left(\sin^2a+cos^2a\right)^3-3\cdot\sin^2a\cdot cos^2a\left(\sin^2a+cos^2a\right)\right\rbrack\)
\(=3\left\lbrack1-2\cdot\sin^2a\cdot cos^2a\right\rbrack-2\cdot\left\lbrack1-3\cdot\sin^2a\cdot cos^2a\right\rbrack\)
\(=3-6\cdot\sin^2a\cdot cos^2a-2+6\cdot\sin^2a\cdot cos^2a\)
=3-2
=1
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