Solve the equation on the interval [0, 2π). cos x + 2 cos x sin x = 0

Solution:

Given, the equation is cos x + 2 cos x sin x = 0

We have to solve the equation on the interval (0,2π)

Taking out cos x,

cos x(1 + 2sin x) = 0

Now, cos x = 0

x = cos^-1(0)

On solving,

x = π/2 or 3π/2

Now, 1 + 2sin x = 0

2sin x = -1

sin x = -1 / 2

x = sin^-1(-1 / 2)

On solving,

x = 7π / 6 or 11π / 6

Therefore, the solution is x = π / 2, 3π / 2, 7π / 6 and 11π / 6.

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Solve the equation on the interval [0, 2π). cos x + 2 cos x sin x = 0

Summary:

The solutions for the equation cos x + 2cos x sin x = 0 on the interval (0, 2π) are π / 2, 3π / 2, 7π / 6 and 11π / 6.