Question

Prove that sin5θ + sinθ = 2 sin3θ cos 2θ

Answer 1

Answer:

As sin(+sin1)=2sin

2

(+1)

cos

2

(−1)

⇒sin5θ+sinθ=2sin3θcos2θ=sin3θ

⇒sin3θ(2cos2θ−1)=0

⇒sin3θ=0

⇒3θ=nπ

⇒θ=

3

nπ

or 2cos2θ−1=0

⇒cos2θ=

2

1

⇒2θ=2nπ±

3

π

⇒θ=nπ±

6

π

.

Answer 2

As sin(+sin1)=2sin

2

(+1)

cos

2

(−1)

⇒sin5θ+sinθ=2sin3θcos2θ=sin3θ

⇒sin3θ(2cos2θ−1)=0

⇒sin3θ=0

⇒3θ=nπ

⇒θ=

3

nπ

or 2cos2θ−1=0

⇒cos2θ=

2

1

⇒2θ=2nπ±

3

π

⇒θ=nπ±

6

π

.