Question

find the real θ such that 3+2isinθ/1-2isinθ is purely real​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

1−2isinθ

3+2isinθ

=

(1+2isinθ)(1−2isinθ)

(3+2isinθ)(1+2isinθ)

=

1−4i

2

sin

2

θ

3+2isinθ+6isinθ+4i

2

sin

2

θ

=

1+4sin

2

θ

3+8isinθ−4sin

2

θ

=

1+4sin

2

θ

3−4sin

2

θ+8isinθ

8sinθ=0⇒sinθ=0

θ=nπ