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Question

The equation 3sinx+cosx=4 has

A
only one solution
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B
two solutions
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C
infinitely many solutions
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D
no solution
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Solution

The correct option is D no solution
a cosx+bsinx=c
Since, we know that for the above equation to have solutions,
the necessary condition is,
|c|a2+b2
Hence, given equation is
3sinx+cosx=4
a2+b2=12+(3)2=4=2
but, |c|=4
|c|>a2+b2
the given equation has no solution.

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