Question

If 2 sin(θ+3π)=cos(θ−3π ), and tanθ+3=0​

Answer 1

Answer:

option 'D' is correct.

Step-by-step explanation:

ANSWER

secθ+tanθ=

3

⇒1+sinθ=

3

cosθ⇒

3

cosθ−sinθ=1⇒

2

3

cosθ−

2

1

sinθ=

2

1

⇒cos

6

π

cosθ−sin

6

π

sinθ=

2

1

⇒cos(

6

π

+θ)=cos

3

π

therefore general solution is given by,

θ=2nπ−

6

π

±

3

π

⇒θ=2nπ+

6

π

and θ=2nπ−

2

π

but θ=2nπ−

2

π

, which does not satisfy the given equation.

Hence solution in 0≤θ≤3π is,

θ=

6

π

and

6

13π

Hence, option 'D' is correct.