Question

cospower 5 theta= A cos theta +B cos 3 theta+ C cos 5 theta


​

Answer 1

Step-by-step explanation:

search-icon-header

Search for questions & chapters

search-icon-image

Question

Bookmark

If cos5θ=acosθ+bcos

3

θ+ccos

5

θ+d, then

Medium

Solution

verified

Verified by Toppr

Correct option is B)

cos5θ=cos(4θ+θ)=cos4θcosθ−sin4θsinθ=(2cos

2

θ−1)

2

−2sin2θcos2θsinθ

=[2(2cos

2

θ−1)

2

−1]cosθ−4sinθcosθ(2cos

2

θ−1)sinθ(2cos

2

θ−1)sinθ

=[2(4cos

2

θ−4cos

2

θ+1)−1]cosθ−4sin

2

θ(2cos

3

θ−cosθ)

=8cos

5

θ−8cos

3

θ+cosθ−4(1−cos

2

θ)(2cos

3

θ−cosθ)

=8cos

5

θ−8cos

3

θ+cosθ−4(2cos

3

θ−2cos

5

θ−cosθ)

=16cos

5

θ−20cos

3

θ+5cosθ

Hence, a=5,b=−20,c=16,d=0

∴a=b+c+d=1