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Question

Number of solutions in [-1, 1], of the equation sin123x+sin153x=sin1x is:

A
1
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B
2
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C
3
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D
5
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Solution

The correct option is C 3
Trivially x = 0 satisfies the equation
sin12x3+sin1x53=sin1x...(1)
For x0 on taking sine of both sides, we get
2x315x29+x5314x29=x295x2+594x2=9[x0]4(95x2)+813695x2=5(94x2)72=3695x24=95x25x2=5x=±1
On verification, we can easily show that x = 1 and - 1 both satisfy the equation (1).

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