The solutions to cos is 60°, 180°, 300°.
A trigonometric equation is what?
An equation with one or more trigonometric ratios of unknown angles is said to as trigonometric.
The ratios of sine, cosine, tangent, cotangent, secant, and cosecant angles are used to express it. A trigonometric equation is cos2 x + 5 sin x = 0, for instance.
Given,
cos (x/2) - sin (x) = 0
⇒ cos (x/2) - 2sin (x/2) cos (x/2) = 0
⇒ cos (x/2) [1 - 2sin (x/2)] = 0
Therefore, cos (x/2) = 0 = cos (90°) (x/2 can't be 270°)
⇒ x = 180°
Again, [1 - 2sin (x/2)] = 0
⇒ 2sin (x/2) = 1
⇒ sin (x/2) = 1/2
⇒ (x/2) = 30°, 150°
⇒ x = 60°, 300°
The solutions to cos is 60°, 180°, 300°.
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