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=1−tan2A1+tan2A cos2A+sin2B=1−tan2A1+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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