Homework SourseVerify the identity cos4x18sin2x8sin4xSolutiongiven cos4x 1
Verify the identity: cos4x=1-8sin2x+8sin4x
Solution
given cos4x = 1 -8sin2x + 8sin4x
L.H.S= cos4x
=cos(2.2x)
= [1 -2sin^2(2x)]
= [ 1 - 2(2sinx.cosx)^2 ]
= [ 1 - 2(4sin^2x .cos^2x) ]
=[ 1 -8sin^2x.(1-sin^2x) ]
= 1 -8sin^2x + 8sin^4x
so L.H.S=R.H.S
HENCE PROVED
COMMNENT IF U DON\'T UNDERSTAND
![Verify the identity: cos4x=1-8sin2x+8sin4xSolutiongiven cos4x = 1 -8sin2x + 8sin4x L.H.S= cos4x =cos(2.2x) = [1 -2sin^2(2x)] = [ 1 - 2(2sinx.cosx)^2 ] = [ 1 - 2](/WebImages/3/verify-the-identity-cos4x18sin2x8sin4xsolutiongiven-cos4x-1-970621-1761499513-0.webp "Verify the identity: cos4x=1-8sin2x+8sin4xSolutiongiven cos4x = 1 -8sin2x + 8sin4x L.H.S= cos4x =cos(2.2x) = [1 -2sin^2(2x)] = [ 1 - 2(2sinx.cosx)^2 ] = [ 1 - 2")
