The number of solutions of the equation sin x ⋅ sin 2 x ⋅ sin 3 x ⋅ sin 4 x ⋅ sin 5 x = 0 in 0 , π is equal to

Question

The number of solutions of the equation sin x ⋅ sin 2 x ⋅ sin 3 x ⋅ sin 4 x ⋅ sin 5 x = 0 in 0 , π is equal to,

MARKS App · Accepted Answer

Note sin ⁡ 4 x = 0 contains all solutions of sin ⁡ x = 0 , sin ⁡ 2 x = 0 sin ⁡ 4 x = 0 ⇒ x = 0 , π 4 , π 2 , 3 π 4 , π sin ⁡ 3 x = 0 ⇒ x = 0 , π 3 , 2 π 3 , π sin ⁡ 5 x = 0 ⇒ x = 0 , π 5 , 2 π 5 , 3 π 5 , 4 π 5 , π Hence, the number of solutions = 11

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