if tan^2A=1+2tan^2B prove that, cos2B=1+2cos2A

Soln:-  Tan^2A=1+2Tan^2B
       or,  Sec^2A-1 = 1+2(Sec^2B-1)
       or,  Sec^2A = 1+2sec^2B-2+1
       or,  (1/Cos^2A)=(2/Cos^2B)
       or,  Cos^2B=2Cos^2A  
       or,  (1+Cos2B)/2=1+Cos2A
       or,  1+Cos2B=2(1+Cos2A)
      or,  Cos2B=2+2Cos2A-1
      or,  Cos2B=1+2CosA
Hence L.H.S=R.H.S Proved
  • 8
4x+5x=460
5x+4x=440 find x and y
  • -6
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