Respuesta :

gmany

[tex] \sin2x-\cos x=0\ \ \ |\text{use:}\ \sin2x=2\sin x\cos x\\\\2\sin x\cos x-\cos x=0\\\\\cos x(2\sin x-1)=0\iff\cos x=0\ \vee\ 2\sin x-1=0\\\\(1)\ \cos x=0\to x=90^0\ \vee\ x=270^o\\\\(2)\ 2\sin x-1=0\ \ \ |+1\\2\sin x=1\ \ \ |:2\\\sin x=\frac{1}{2}\to x=30^o\ \vee\ x=150^o\\\\Answer:\ B.)\ 90^o. [/tex]

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The solution to the equation sin(2x) - cos(x) = 0 is Option (B) 90°.

What is solution of a trigonometric equation ?

The solution of any trigonometric equation represents the value of the parameter which satisfies the given equation. The solution should lie within a given range and it should have the same value as ±π .

How to find the solution of the given trigonometric function ?

Given expression is sin(2x) - cosx = 0

Using formula, sin(2x) = 2sinxcosx

We have , 2sinxcosx - cosx = 0

⇒ cosx(2sinx - 1) = 0

Either cosx = 0

∴ x = π/2 radian or 90°

Or  2sinx - 1 = 0

⇒ 2sinx = 1

⇒ sinx = 1/2

∴ x = π/6 radians or 30°

Thus, the solution to the equation sin(2x) - cos(x) = 0 is Option (B) 90°

To learn more about solution of trigonometric function, refer -

https://brainly.com/question/25618616

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