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Question: If \(\cos 3\theta = \alpha\cos\theta + \beta\cos^{3}\theta,\) then \((\alpha,\beta) =\)...

If cos⁡3θ=αcos⁡θ+βcos⁡3θ,\cos 3\theta = \alpha\cos\theta + \beta\cos^{3}\theta, then (α,β)=(\alpha,\beta) =

A

(3,4)(3,4)

B

(4,3)(4,3)

C

(−3,4)( - 3,4)

D

(3,−4)(3, - 4)

Answer

(−3,4)( - 3,4)

Explanation

Solution

.(3)

Sol. Given that cos⁡3θ=αcos⁡θ+βcos⁡3θ\cos 3\theta = \alpha\cos\theta + \beta\cos^{3}\theta

But cos⁡3θ=4cos⁡3θ−3cos⁡θ\cos 3\theta = 4\cos^{3}\theta - 3\cos\theta ⇒ (α,β)=(−3,4)(\alpha,\beta) = ( - 3,4).