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Trigonometric Ratios for Sum of Two Angles

If cos 3 thet...

Question

If cos 3theta = $α c o s θ + β c o s^{3} θ$ , 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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Similar questions

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

\frac{cos α}{cos θ} + \frac{sin α}{sin θ} = \frac{cos β}{cos θ} + \frac{sin β}{sin θ} = 1

α

β

do not differ by an even multiple of

π

\frac{cos α cos β}{{cos}^{2} θ} + \frac{sin α sin β}{{sin}^{2} θ} + 1 = 0

.

β

α

are +ive angles less than two right angles and

c o s α + c o s (α + β) + c o s (α + β + γ) = 0

s i n α + s i n (α + β) + s i n (α + β + γ) = 0

β = γ = 2 π / 3

α = {cos}^{- 1} (\frac{3}{5}), β = {tan}^{- 1} (\frac{1}{3}),

0 < α, β < \frac{π}{2},

α - β

3 cos θ + 4 sin θ = A sin (θ + α),

A

α

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Trigonometric Ratios for Sum of Two Angles

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