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If tan 2 A=1+2tan 2 B, prove that 2sin 2 A=1+s in 2 B...

  If tan2A=1+2tan2B, prove that        2sin2A=1+sin2B...

Grade:10

1 Answers

Vikas TU
14149 Points
7 years ago
From eqn.  tan2A=1+2tan2B
sin^2A/cos^2A = 1 +2sin^2B/cos^2B
=> sin^2A*cos^2B/cos^2A = cos^2B +2sin^2B
=>  sin^2A*cos^2B = (cos^2B +2sin^2B)*cos^2A
=> sin^2A -sin^2Asin^2B = (1 -sin^2A)(1 + sin^2B) = 1 -sin^2A + sin^2B -sin^2Asin^2B
=> 
 
2sin2A=1+sin2B  H.proved

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