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Question

The number of integral values of p, for which the equation 5cosx+4sinx=2p+3 has real solutions is

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Solution

5cosx+4sinx=2p+3
For the equation to have solution, 2p+3 should lie in the range of 5cosx+4sinx

Now,
52+425cosx+4sinx52+4252+422p+352+42412p+3414132p4134132p4132

Hence, the integral values of p are {4,3,2,1,0,1}

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