A value of θ satisfying sin5θ-sin3θ+sinθ=0, such that 0<θ<π2 is
π12
π6
π4
π2
Explanation for correct answer:
Finding the value.
Step-1: Simplify the given data.
Given, sin5θ-sin3θ+sinθ=0,
⇒ sin5θ+sinθ=sin3θ
Step-2: Apply formula sin(c)+sin(d)=2sin(c+d2)cos(c-d2)
⇒ 2sin5θ+θ2cos5θ-θ2=sin3θ
⇒ 2sin3θcos2θ=sin3θ
⇒ 2sin3θcos2θ-sin3θ=0
⇒ sin3θ2cos2θ-1=0
⇒ sin3θ=0, cos2θ=12
⇒ ππθ=nπ, 2θ=π3 θ=π/6
Hence, option B is correct.