Question

solve: sin2x - 2(sinx+cosx) = 1

Answer 1

Is the first thing sin(2x) or sin^2x ?

Answer 2

sin(2x)

Answer 3

2sinxcosx - 2(sinx + coxx) = 1
Try to think of it like 2xy - 2(x+y) = 1

Answer 4

i think i itried that but it didnt give me anything. ill try it again

Answer 5

This is a special type of trig equation in the form:
a(sin x + cos x) + b*sin x*cos x = c. To solve it, put (sin x + cos x) = t
-> (sin x + cos x)^2 = t^2 = 1 + 2*sin x*cos x -> sin x*cos x = 1/2(t^2 - 1)

Answer 6

2*sin x*cos x - 2(cos x + sin x) - 1 = 0
(t^2 - 1) - 2t - 1 = 0
t^2 - 2t - 2 = 0.
D = 4 + 8 = 12 = 4*3 -> VD = 2V3 and -2V3
t1 = 2 + V3 (rejected because > 2), and t2 = 2 - V3 = 0.27
We know that (sin x + cos x) = t = V2*sin (x + Pi/4)-->
sin (x + Pi/4) = 0.27/V2 = 0.19 = sin 10.95 deg
x1 = 10.95 - 45 = - 34.05 = or (360 - 34.05) = 325.95 deg,
and x2 = 180 + 34.05 = 214.50 deg