51I'm Using A and B in place of Alpha and Beta respectively,
tan2A= 1+ tan2B + tan2B
=> tan2A - tan2B = 1+ tan2B
=> sin2Acos2A - sin2Bcos2B = 1 + sin2Bcos2B
=> sin2Acos2B - sin2Bcos2Acos2A cos2B = 1cos2B
=> (sinAcosB)2 - (sinBcosA)2 = cos2A
=> cos2A = sin(A+B)sin(A-B)
=> cos2A = cos2B - cos2A
=> 2cos2A -1 = cos2B -1
=> 2cos2A= (2cos2B -1) -1
=> 2cos2A +1 = cos2B
Proved. :)
Manish Sarkar i could not undrstnd the 2nd last step..
Upvote·0· Reply ·2013-07-19 19:34:11- Aniq Ur Rahman in the third last step, multiply both sides with 2
then break the -2 on RHS into -1 and -1, Apply the formula of Multiple angles and you'll get the last step.
- Aniq Ur Rahman in the 2nd step, we can simply use 1 =tan2B = sec2B => 1/cos2B
