Answer:
(1+sin2A+cos2A) ^2=4cos^2A(1+sin2A)
Step-by-step explanation:
Here,
L.H.S=(1+sin2A+cos2A)^2
=(1+2sinAcosA+2cos^2A-1)^2
=(2sinAcosA+2cos^2A)^2
={2cosA(sinA+cosA)}^2
=4cos^2A(sinA+cosA)^2
=4cos^2A(sin^2A+2sinA.cosA+cos^2A)
=4cos^2A(sin^2A+cos^A+2sinAcosA)
=4cos^2A(1+sin2A)
=R.H.S
Hence,L.H.S=R.H.S.
(1+sin2A+cos2A)^2=4cos^2A(1+sin2A).
proved.
