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Question

(1+tanAtanB)2+(tanAtanB)2=sec2Asec2B.

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Solution

Given:

(1+tanAtanB)2+(tanAtanB)2

=1+2tanAtanB+tan2Atan2B+tan2A2tanAtanB+tan2B

=1+tan2A+tan2Atan2B+tan2B

=sec2A+tan2B(tan2A+1)

=sec2A+tan2Bsec2A

=sec2A(1+tan2B)

=sec2Asec2B


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