Answer:
General solution
θ =[tex]\frac{2n\pi }{3} +\frac{\pi }{2}[/tex]
Put n=1
θ = 210°
put n =2
θ = 330°
put n=3
θ = 270°
Step-by-step explanation:
Explanation:-
Given equation
sin 2θ cosθ + cos 2θ sinθ = -1
we know that
Sin (A+B) = sin A cos B +Cos A sin B
sin( 2θ+θ) = sin (180+90)
= [tex]Sin(\pi +\frac{\pi }{2})[/tex]
sin 3θ = sin (3π/2)
General solution of sinθ = sinα
θ = 2 n π ±α
3θ = 2 n π ±3π/2
θ =[tex]\frac{2n\pi }{3} +\frac{3\pi }{6}[/tex]
θ =[tex]\frac{2n\pi }{3} +\frac{\pi }{2}[/tex]
Put n=1
θ=[tex]\frac{2\pi }{3} +\frac{\pi }{2}=\frac{4\pi +3\pi }{6} =\frac{7\pi }{6}[/tex] = 210°
put n =2
θ=[tex]\frac{4\pi }{3} +\frac{\pi }{2}=\frac{8\pi +3\pi }{6} =\frac{11\pi }{6}[/tex] = 330°
Put n=3
θ=[tex]\frac{2 (3)\pi }{3} +\frac{\pi }{2}=2\pi +\frac{\pi }{2} = \frac{3\pi }{2}[/tex] = 270°
