Question

expansion of cos4theta​

Answer 1

Answer:

Since cos(4θ)=2cos2(2θ)−1 and cos(2θ)=1−sin2(θ), we have cos(4θ)−4cos(2θ)=2cos2(2θ)−4cos(2θ)−1=2(1−2sin2(θ))2−4(1−2sin2(θ))−1=2−8sin2(θ)+8sin4(θ)−4+8sin2(θ)−1=8sin4(θ)−3.

Answer 2

Answer:

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Step-by-step explanation:

cos

4

θ

=(cos

2

θ)

2

=

4

1

(1+cos2θ)

2

=

4

1

[1+cos

2

2θ+2cos2θ]

=

4

1

[1+

2

1+cos4θ

+2cos2θ]

=

8

1

[2+1+cos4θ+4cos2θ]

=

8

1

[cos4θ+4cos2θ+3]