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Trigonometry question:Prove that-(tanA-tanB) ²+(1+tanAtanB)²=sec²Asec²B

Trigonometry question:Prove that-(tanA-tanB) ²+(1+tanAtanB)²=sec²Asec²B

Grade:10

1 Answers

Shashank Singh
askIITians Faculty 57 Points
3 years ago
on expanding we get
tan^2A + tan^2B -2tanAtanB +1 + tan^2Atan^2B – 2tanAtanB
= 1+tan^2A +tan^2B+tan^2Atan^2B
= sec^2A + tan^2B(1+tan^2A)
= sec^2A + sec^2A tan^2B
= sec^2A(1+tan^2B)
= sec^2Asec^2B …....... [hence proved]

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