Question

9 sinx + cos2x=2a +7 posseses a solution if?​

Answer 1

If the equation asinx+cos2x=2a−7 possesses a solution, then find the value of a.

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Text Solution

Solution :

asinx+cos2x=2a−7

⇒asinx+1−2sin2x=2a−7

⇒2sin2x−asinx+2a−8=0

⇒sinx=a±a2−4(2)(2a−7)−−−−−−−−−−−−−−√4

⇒sinx=a±a2−16a+64−−−−−−−−−−−√4

⇒sinx=a±(a−8)2−−−−−−−√4

⇒sinx=a+a−84andsinx=a−a+84

⇒sinx=a−42andsinx=2

We know, sinx≠2,

∴sinx=a−42

∴−1≤a−42≤1

⇒2≤a≤6

∴a∈[2,6], which is required solution.