Question

Find all exact values of

Answer 1

Answer:

General solution

 θ =$\frac{2n\pi }{3} +\frac{\pi }{2}$

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)

                       = $Sin(\pi +\frac{\pi }{2})$

        sin 3θ = sin (3π/2)

General solution of  sinθ  = sinα

                  θ = 2 n π ±α

                  3θ = 2 n π ±3π/2

                   θ =$\frac{2n\pi }{3} +\frac{3\pi }{6}$

                  θ =$\frac{2n\pi }{3} +\frac{\pi }{2}$

Put n=1

                  θ=$\frac{2\pi }{3} +\frac{\pi }{2}=\frac{4\pi +3\pi }{6} =\frac{7\pi }{6}$ = 210°

put n =2

                  θ=$\frac{4\pi }{3} +\frac{\pi }{2}=\frac{8\pi +3\pi }{6} =\frac{11\pi }{6}$ = 330°

Put n=3

                  θ=$\frac{2 (3)\pi }{3} +\frac{\pi }{2}=2\pi +\frac{\pi }{2} = \frac{3\pi }{2}$  = 270°