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Question
Solve 12sinx+5cosx=2y2−8y+21 to get the values of n and y
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Solution
Given equation is,12sinx+5cosx=2y2−8y+21
As −13≤12sinx+5cosx≤13
2y2−8y+21=−13 or 2y2−8y+21=13
2y2−8y+34=0 or 2y2−8y+8=0
y2−4y+17=0 or y2−4y+4=0
imaginary roots or (y−2)2=0
y=2
12sinx+5cosx=2y2−8y+21
As −13≤12sinx+5cosx≤13
2y2−8y+21=−13 or 2y2−8y+21=13
2y2−8y+34=0 or 2y2−8y+8=0
y2−4y+17=0 or y2−4y+4=0
imaginary roots or (y−2)2=0
y=2
As −13≤12sinx+5cosx≤13
2y2−8y+21=−13 or 2y2−8y+21=13
2y2−8y+34=0 or 2y2−8y+8=0
y2−4y+17=0 or y2−4y+4=0
imaginary roots or (y−2)2=0
y=2
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