12. If n is a positive integer (1+cos +isin o)" +(1+ cos 0 - i sin )" = 2n+l cos"(o/2)cos(o/2)
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ડગઞણઙડઙઞઙણઞઙએચણબઞપણણઙએઉએટઉણઉઈણગઞટગણચણબટણઙડઐઉડઈએડઞઊઈઓચઓચઓચઓચઓઙડઙડઙડઙડચડચઐઇડઇઐચડલબચલઓજ
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1+cosθ+isinθ)
n
+(1+cosθ−isinθ)
n
=(2cos
2
2
θ
+i2sin
2
θ
cos
2
θ
)
n
+(2cos
2
2
θ
−i2sin
2
θ
cos
2
θ
)
n
=2
n
cos
n
2
θ
(e
i
2
nθ
+e
−i
2
nθ
)
=2
n
cos
n
(
2
θ
)(2cos
2
nθ
)
=2
n+1
cos
n
(
2
θ
)cos(
2
nθ
)
please mark as brilliant
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