Question

How do I solve these trigonometric equations!!?

Find all solutions in the interval [0, 2π).

(sin x)(cos x) = 0

Find all solutions in the interval [0, 2π).

cos2x + 2 cos x + 1 = 0

Find all solutions to the equation.

cos2x + 2 cos x + 1 = 0

Answer 1

Solution are

i)
`x = 0, \pi, (3\pi)/(2) , 2\pi`

Explanation:

1) (sinx)(cosx) =0

sin2x/2 =0

2x =0, 2pi, 3pi, 4pi

Hence
`x = 0, \pi, (3\pi)/(2) , 2\pi`

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2)
`cos2x + 2 cos x + 1 = 0\\2cos^2 x +2cosx +1 =0\\(cosx+1)^2 =0\\cosx =-1\\x=\pi`

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