Cosine 4 theta equals what in terms of cosine theta?

Question

Cosine 4 theta equals what in terms of cosine theta?

Answer 1

Cos4T

=Cos^2 2T - sin^2 2T

=(2cos^2 T - 1)^2 - (2sinTcosT)^2

=4cos^4 T - 2cos^2 T + 1 - 4sin^2 Tcos^2 T

=4cos^4 T - 2cos^2 T + 1 - 4(1-cos^2 T)cos^2 T

= 8cos^4 T - -6cos^2 T +1

Answer 2

cos(4theta)

=cos(2theta+.2theta)

=cosinesquare(2theta)-sinesquare(2thet...

=1-sinesquare(2theta)-sinesquare(2thet...

=1-2sinesquare(2theta)

=1-2(2sine theta.cosine theta)^2

=1-8sinesquare theta.cosinesquare theta

Answer 3

Just use the identity cos(2θ) = 2cos^2(θ) - 1, and apply it twice.

cos(4θ) =

cos(2*(2θ)) =

2cos^2(2θ) - 1 =

2[ 2cos^2(θ) - 1 ]^2 - 1

2 [ 4cos^4(θ) - 4cos^2(θ) + 1 ] - 1

8cos^4(θ) - 8cos^2(θ) + 1