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Question

If A+B=45, prove that (1+tanA)(1+tanB)=2 and hence deduce that tan2212=21

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Solution

A+B=450
A=450B
tanA=tan(450B)=1tanB1+tanB
tanA+1=1tanB1+tanB+1=21+tanB
(1+tanA)(1+tanB)=2
Now, for A=B=2212
(1+tanA)2=2
tanA=tan(2212)=21

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