To find the solutions to the equation:
(2sin(x+π/6) - 1)(2tan(x) + 1) = 0
We set each factor equal to zero and solve for x:
1) 2sin(x+π/6) - 1 = 02sin(x+π/6) = 1sin(x+π/6) = 1/2
Using the reference angle of π/6 in the first quadrant where sine is positive, we have:x+π/6 = π/6 + 2πn or x+π/6 = 5π/6 + 2πn
This simplifies to:x = 0 + 2πn or x = π/2 + 2πn
2) 2tan(x) + 1 = 02tan(x) = -1tan(x) = -1/2
Using the reference angle of π/6 in the fourth quadrant, we have:x = 5π/6 + πm
So the solutions to the equation are:x = 0 + 2πn, π/2 + 2πn, 5π/6 + πm where n and m are integers.
To find the solutions to the equation:
(2sin(x+π/6) - 1)(2tan(x) + 1) = 0
We set each factor equal to zero and solve for x:
1) 2sin(x+π/6) - 1 = 0
2sin(x+π/6) = 1
sin(x+π/6) = 1/2
Using the reference angle of π/6 in the first quadrant where sine is positive, we have:
x+π/6 = π/6 + 2πn or x+π/6 = 5π/6 + 2πn
This simplifies to:
x = 0 + 2πn or x = π/2 + 2πn
2) 2tan(x) + 1 = 0
2tan(x) = -1
tan(x) = -1/2
Using the reference angle of π/6 in the fourth quadrant, we have:
x = 5π/6 + πm
So the solutions to the equation are:
x = 0 + 2πn, π/2 + 2πn, 5π/6 + πm where n and m are integers.