How to find all solutions of equation (2*cosx-square root3)(11sinx-9)=0?
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We have to find the solutions of the equation: (2*cos x - sqrt 3) (11*sin x - 9 ) = 0.
If 2*cos x - sqrt...
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We'll start from the fact that a product is zero if one of it's factors is zero.
We'll set the first factor as zero.
2*cosx-sqrt3 = 0
We'll add sqrt3 both sides:
2cos x = sqrt3
cos x = sqrt3/2
x = +/-arccos(sqrt3/2) + 2kpi, k is an integer number
x = +/-(pi/6) + 2kpi
Let's put the next factor equal to zero.
11sinx-9 = 0
We'll add 9 both sides:
11sin x = 9
We'll divide by 11:
sin x = 9/11
x = (-1)^k*arcsin(9/11) + k*pi
The solutions of the equation are: {+/-(pi/6) + 2kpi} U {(-1)^k*arcsin(9/11) + k*pi}.
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