Find the general value of theta which satisfies the equation (costheta+isintheta)(cos3theta+isin3theta)(cos5theta+isin5theta)...
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Proof is given below.
Explanation:
cos
3
θ
=
cos
(
2
θ
+
θ
)
=
cos
2
θ
cos
θ
−
sin
2
θ
sin
θ
=
(
cos
2
θ
−
sin
2
θ
)
cos
θ
−
2
sin
θ
cos
θ
sin
θ
=
cos
3
θ
−
sin
2
cos
θ
−
2
sin
2
θ
cos
θ
=
cos
θ
(
cos
2
θ
−
sin
2
θ
−
2
sin
2
θ
)
=
cos
θ
(
cos
2
θ
−
3
sin
2
θ
)
=
cos
3
θ
−
3
sin
2
θ
cos
θ
=
cos
3
θ
−
3
(
1
−
cos
2
θ
)
cos
θ
=
cos
3
θ
−
3
cos
θ
+
3
cos
3
θ
=
4
cos
3
θ
−
3
cos
θ
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