Number of solutions in [-1, 1], of the equation sin−123x+sin−1√53x=sin−1x 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 sin−12x3+sin−1x√53=sin−1x...(1)
For x≠0 on taking sine of both sides, we get 2x3√1−5x29+x√53√1−4x29=x⇒2√9−5x2+√5√9−4x2=9[∵x≠0]⇒4(9−5x2)+81−36√9−5x2=5(9−4x2)⇒72=36√9−5x2⇒4=9−5x2⇒5x2=5⇒x=±1
On verification, we can easily show that x = 1 and - 1 both satisfy the equation (1).