Remark Change all the trig functions to sin's
Solution
4(1 - sin^2(x)) = 5 - 4sin(x) Remove the brackets.
4 - 4*sin^2(x) = 5 - 4sin(x) Let y = sin(x)
4 - 4y^2 = 5 - 4y Add 4y^2 to both sides; Subtract 4 from both sides.
0 = 5 -4 - 4y + 4y^2
0 = 1 - 4y + 4y^2 'factor
0 = (1 - 2y)^2 Take the square root of both sides.
sqrt(1 - 2y)^2 = sqrt(0)
1 - 2y = 0 Subtract 1 from both sides
-2y = - 1 Divide by - 2
y = -1/-2
y = 1/2 Let sin(x) = y
Sin(x) = 1/2 There are 2 places where sin(x) = 1/2
x = sin-1(1/2)
x = 30o
x = 180 - 30 = 150
Note: the sine function is positive in quadrants 1 and 2. In quadrant 2, the sine function is found by 180 - x. In this case since x = 30, then the other angle giving sin(X) = 1/2 is 180 - 30 = 150
Answer
x = 30
x = 150