SATHEE: Trigonometrical Equations 1 Question 7

Trigonometrical Equations 1 Question 7

7. If $0 \leq x < \frac{π}{2}$ , then the number of values of $x$ for which $\sin x - \sin 2 x + \sin 3 x = 0$ , is

(a) 2

(b) 3

(d) 4

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Answer:

Correct Answer: 7. (a)

Solution:

We have, $\sin x - \sin 2 x + \sin 3 x = 0$

$\Rightarrow (\sin x + \sin 3 x) - \sin 2 x = 0$

$\Rightarrow 2 \sin \frac{x + 3 x}{2} \cos \frac{x - 3 x}{2} - \sin 2 x = 0$

$[∵ \sin C + \sin D = 2 \sin \frac{C + D}{2} \cos \frac{C - D}{2}]$

$\begin{array}{lrl} \Rightarrow & 2 \sin 2 x \cos x - \sin 2 x = 0 & [∵ \cos (- θ) = \cos θ] \\ \Rightarrow & \sin 2 x (2 \cos x - 1) = 0 \\ \Rightarrow & \sin 2 x = 0 or 2 \cos x - 1 = 0 \\ \Rightarrow & 2 x = 0, π, \dots or \cos x = \frac{1}{2} \\ \Rightarrow & x = 0, \frac{π}{2} \dots or x = \frac{π}{3} \end{array}$

In the interval $0, \frac{π}{2}$ only two values satisfy, namely $x = 0$ and $x = \frac{π}{3}$ .

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Trigonometrical Equations 1 Question 7

7. If 0≤x<π2, then the number of values of x for which sin⁡x−sin⁡2x+sin⁡3x=0, is

Answer:

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7. If $0 \leq x < \frac{π}{2}$ , then the number of values of $x$ for which $\sin x - \sin 2 x + \sin 3 x = 0$ , is