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Question

If 3sinx+4cosax=7 has at least one solution and a=pmqn+1; where m,nZ, then the value of p+q is

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Solution

We have 3sinx+4cosax=7 which is possible only when sinx=1 and cosax=1
x=(4n+1)π2 and ax=2mπ
x=(4n+1)π2=2mπa
a=4m4n+1=pmqn+1
p+q=4+4=8

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