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Q.

The trigonometric form of z=(1−i  cot  8)3  (where i=−1 ) is

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a

cosec3 8.ei(24−3π/2)

b

cosec3 8.e−i(24−3π/2)

c

cosec3 8.ei(36−π/2)

d

cosec2 8.e−24i+π/2

answer is A.

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Detailed Solution

z=(1−i  cot8)3 =cosec38(sin8−i  cos8)3                         =cosec38(cos(π2−8)−i  sin(π2−8))3                                 =cosec38(cos(3π2−24)−i  sin(3π2−24))=cosec38.e−i(3π/2−24)=cosec38.ei(24−3π/2)
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