Question

Find all exact values of

If there are multiple solutions, list the solutions in numerical order separated by commas. If there is no solution, use Ø.
Provide your answer below:​

Answer 1

General solution

θ =
`(2n\pi )/(3) +(\pi )/(2)`

Put n=1

θ = 210°

put n =2

θ = 330°

put n=3

θ = 270°

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 +(\pi )/(2))`

sin 3θ = sin (3π/2)

General solution of sinθ = sinα

θ = 2 n π ±α

3θ = 2 n π ±3π/2

θ =
`(2n\pi )/(3) +(3\pi )/(6)`

θ =
`(2n\pi )/(3) +(\pi )/(2)`

Put n=1

θ=
`(2\pi )/(3) +(\pi )/(2)=(4\pi +3\pi )/(6) =(7\pi )/(6)` = 210°

put n =2

θ=
`(4\pi )/(3) +(\pi )/(2)=(8\pi +3\pi )/(6) =(11\pi )/(6)` = 330°

Put n=3

θ=
`(2 (3)\pi )/(3) +(\pi )/(2)=2\pi +(\pi )/(2) = (3\pi )/(2)` = 270°