Question

If θ =
/3
, find the value of cosθ + cos2θ + cos3θ + cos4θ + cos5θ cos6θ

Answer 1

Step-by-step explanation:

ANSWER

Combining cosθ and cos3θ.

(cosθ+cos3θ)+cos2θ=0

2cos2θcosθ+cos2θ=0

or cos2θ(2cosθ+1)=0

∴cos2θ=0=cos(π/2),

∴2θ=(n+

2

1

)π,

or θ=(2n+1)π/4

2cosθ+1=0

∴cosθ=−1/2=−cos(π/3)

=cos(π−π/3)=cos(2π/3)

∴θ=2nπ±2π/3.

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