Question

Find the principal value of cosx=0​

Answer 1

Answer:

Cos 0° = 1

cos x = 0, when x = ±π/2, ±3π/2, ±5π/2, … It means that cos x vanishes when x is an odd multiple of π/2. So, cos x = 0 implies x = (2n + 1)π/2 , where n takes the value of any integer.

Answer 2

Hence, the general solution for sin x = 0 will be, x = nπ, where n∈I. Similarly, general solution for cos x = 0 will be x = (2n+1)π/2, n∈I, as cos x has a value equal to 0 at π/2, 3π/2, 5π/2, -7π/2, -11π/2 etc.

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