Question

cos theta = n cos (theta + pi) prove ( n+1)tan(theta+pi)=(n-1)cot pi​

Answer 1

Answer:

(1+cosθ+isinθ)n=[2cos22θ​+i2sin2θ​cos2θ​]n=[2cos2θ​(cos2θ​+isin2θ​)]n

=2ncosn2θ​(cos2nθ​+isin2nθ​) ....(1)

Replacing i by −i we get,

(1+cosθ−isinθ)n=2ncosn2θ​(cos2nθ​−isin2nθ​) ....(2)

Adding equations (1) and (2), we get

(1+cosθ+isinθ)n+(1+cosθ−isinθ)n=2ncosn2θ​(2cos2nθ​)

=2n+1cosn2θ​.cos2nθ​

Hence, proved.

Step-by-step explanation:

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