Question

If sin 5x+sin 3x+sin x = 0, then the value of x other than zero, lying between π0≤×≤π2 is;

• A. (A) ππ6
• B. (B) ππ12
• C. (C) ππ3
• D. (D) ππ4

Answer 1

Answer: (C)

(C) ππ3

Answer 2

Explanation:
Given:A trigonometric equation, sin⁡5x+sin⁡3x+sin⁡x=0,We have to find the value of x other than zero lying between 0≤x≤π2Consider,sin⁡5x+sin⁡3x+sin⁡x=0⇒(sin⁡x+sin⁡5x)+sin⁡3x=0⇒2sin⁡3xcos⁡2x+sin⁡3x=0[∵sin⁡C+sin⁡D=2sin⁡(C+D2)cos⁡(C−D2)]⇒sin⁡3x(2cos⁡2x+1)=0⇒sin⁡3x=0 or 2cos⁡2x+1=0But cos⁡2x≠−12 for x∈[0,π2]Thussin⁡3x=0⇒3x=π⇒x=π3Hence, the correct option is (C).