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Question

If tan2A=2tan2B+1 then the value of cos2A+sin2B.


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Solution

We are given tan2A=2tan2B+1

We want to find cos2A+sin2B

We are given the value of tan2A.So, write the value of cos2A in terms of tanA

cos2A=1tan2A1+tan2A

cos2A+sin2B=1tan2A1+tan2A+sin2B

Substituting the value of tan2A

= 1(2tan2B+1)1+2tan2B+1+sin2B

= 2tan2B2(1+tan2B+sin2B

= 2tan2Bsec2B+sin2B

= sin2B+sin2B

= 0


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