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Trigonometric Ratios for Sum of Two Angles

If cos3θ = α ...

Question

If $c o s 3 θ$ = $α c o s θ + β c o s^{3} θ$ , then $(α, β)$ =

A

(3,4)

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B

(4,3)

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C

(-3,4)

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D

(3,-4)

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Solution

The correct option is C
(-3,4)

Given that $c o s 3 θ = α c o s θ + β c o s^{3} θ$

But $c o s 3 θ = 4 c o s^{3} θ - 3 c o s θ$ $\Rightarrow$ $(α, β)$ = (-3, 4).

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