Question

The number of solutions for the equation 3cos theta - 4cos^3 theta=1 in theta belongs to [-pi, pi]​

Answer 1

Given:

(- 4cos³θ + 3cosθ)= 1

To find:

Number of Solutions in [-π,π]

Step-by-step explanation:

=> 4cos³θ−3cosθ= -1

=> cos3θ= -1

=> 3θ = Cos-1 (-1)

=> 3θ = (2n+1)π

=> θ = (2n+1)π/3

For n= -2, -1, 0, 1

=> θ = -π, -π/3, π/3, π

Respectively

Therefore, there are 4 solutions in [-π,π]

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