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If tan^2A = 1+ 2tan^2B then prove that cos^2 B=2 cos^2 A

Taniya Ray , 8 Years ago
Grade 10
anser 3 Answers
Arun
Dear Taniya
 
tan^2 A = 1 + 2tan^2 B 
=> sin^2 A / cos^2 A = 1 + 2 sin^2 B / cos^2 B 
=> sin^2 A / cos^2 A = (cos^2 B + 2sin^2 B) / cos^2 B 
=> sin^2 A cos^2 B = cos^2 A (cos^2 B + 2 sin^2 B) 
=> sin^2 A (1 - sin^2 B) = (1 - sin^2 A) (1 - sin^2 B + 2 sin^2 B) 
=> sin^2 A - sin^2 A sin^2 B = (1 - sin^2 A) (1 + sin^2 B) 
=> sin^2 A - sin^2 A sin^2 B = 1 - sin^2 A + sin^2 B - sin^2 A sin^2 B 
=> 2 sin^2 A = 1 + sin^2 B 
 
2 - 2 sin^2 A = 2 -(1 + sin^2 B)
2 cos^2 A = cos^2 B
 
Regards
Arun (askIITians forum expert)
Last Activity: 8 Years ago
Vikas TU
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