find all the values:
sin2x- sqrt3cosx=0
sin 2x = 2 sin x cos x
so
2 sin x cos x - sqrt 3 * cos x = 0
cos x * (2 sin x - sqrt 3 ) = 0
well, if cos x = 0, that works so
x = pi/2 (90deg) or x = 3 pi/2(270 degrees)
also if
sin x = (1/2) sqrt 3
that is 60 degrees or 120 degrees (30,60, 90 triangle)
Do you mean sin^2x or sin(2x) ?
Do you mean (sqrt3)*cosx
or sqrt(3cosx) ?
To find all the values of x that satisfy the equation sin2x - √3cosx = 0, we will use the trigonometric identity sin2x = 2sinxcosx. Substituting this into the equation, we get:
2sinxcosx - √3cosx = 0
Now, we can factor out the common term cosx:
cosx(2sinx - √3) = 0
This equation will be satisfied if either cosx = 0 or 2sinx - √3 = 0.
First, let's solve for cosx = 0. The solutions for this equation occur when x is π/2 + πn, where n is an integer.
Next, we solve for 2sinx - √3 = 0:
2sinx = √3
sinx = √3 / 2
Using the unit circle or trigonometric identities, we find the solutions for sinx = √3 / 2 occur when x is π/3 + 2πn or 5π/3 + 2πn, where n is an integer.
Therefore, the values of x that satisfy the equation sin2x - √3cosx = 0 are:
x = π/2 + πn, π/3 + 2πn, or 5π/3 + 2πn, where n is an integer.