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
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