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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Trigonometric Equations

NTA Abhyas 2020 · Mathematics · Trigonometric Equations

The number of solutions of the equation x ⋅ 2x ⋅ 3x ⋅ 4x ⋅ 5x = 0...

The number of solutions of the equation \sin x ⋅ \sin 2x ⋅ \sin 3x ⋅ \sin 4x ⋅ \sin 5x = 0 in [0,π]\left[0, \pi\right] is equal to

Correct answer

11

Step-by-step solution

Note sin⁡4x=0\sin 4x = 0 contains all solutions of sinx=0,sin x = 0, sin⁡2x=0\sin 2x = 0
sin⁡4x=0⇒x=0,π4,π2,3π4,π\sin 4x = 0 ⇒ x = 0, \dfrac{\pi}{4}, \dfrac{\pi}{2}, \dfrac{3\pi}{4}, \pi
sin⁡3x=0⇒x=0,π3,2π3,π\sin 3x = 0 ⇒ x = 0, \dfrac{\pi}{3}, \dfrac{2\pi}{3}, \pi
sin⁡5x=0⇒x=0,π5,2π5,3π5,4π5,π\sin 5x = 0 ⇒ x = 0, \dfrac{\pi}{5}, \dfrac{2\pi}{5}, \dfrac{3\pi}{5}, \dfrac{4\pi}{5}, \pi
Hence, the number of solutions =11= 11
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