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Question

4sinxcosy+2cosy+1=0 where x,y[0,2π] find the largest possible value of the sum (x+y).

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Solution

4sinxcosy+2cosy+1=0 x,y[0,2π]
16sin2xcos2y=4cos2y+4cosy+1
16cos2y16cos2xcos2y=4cos2y+4cosy+1
12cos2y4cosy1=16cos2xcos2y
124secysec2y=16cos2x
sec2y4secy+12=16cos2x
Maximum possible values of x and y that satisfies equation are at x=2π and y=4π3
Maximum value of x+y=10π3

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