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Prove that sin ^(2) A cos ^(2) B+cos ^(2...

Prove that `sin ^(2) A cos ^(2) B+cos ^(2) A sin ^(2) B+cos ^(2) A cos ^(2) B+sin ^(2) A sin ^(2) B=1`

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L. .H . S=sin ^(2) A cos ^(2) B+cos ^(2) A sin ^(2) B+cos ^(2) A . cos ^(2) B+sin ^(2) A sin ^(2) B.
.=(sin ^(2) A cos ^(2) B+cos ^(2) A cos ^(2) B)+(cos ^(2) A sin ^(2) B+sin ^(2) A sin ^(2) B).
.=cos ^(2) B(sin ^(2) A+cos ^(2) A)+sin ^(2) B(cos ^(2) A+sin ^(2) A).
.=cos ^(2) (~B)+sin ^(2) (~B)=1=(R) . (H) . (S) ..
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