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Question
Select the correct option from the given alternatives:
If cos pθ = cos qθ, p ≠ q, then ______.
Options
θ = `(2npi)/(p +- q)`
θ = 2nπ
θ = 2nπ ± p
θ = 2nπ ± q
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Solution
If cos pθ = cos qθ, p ≠ q, then, θ = `bb(underline((2npi)/(p +- q))`
Explanation:
Given, cos pθ = cos qθ
cos pθ – cos qθ = 0
`2sin((pθ + qθ)/2) sin((pθ - qθ)/2)` = 0 ...(cos C – cos D)
`sin((pθ + qθ)/2)` = 0 or `sin ((pθ - qθ)/2)` = 0
`(pθ + qθ)/2` = nπ or `(pθ - qθ)/2` = nπ
θ = `(2nπ)/((p + q))` or `(2nπ)/((p - q))` = θ
∴ θ = `(2nπ)/(p +- q)`
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