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Question

If cos2x=cos4x then find the minimum and maximum value of sin2x+cos4x, for all real values of θ

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Solution

cos2x=cos4x(1)
Adding sin2x in both side of equation (1) we get,
Sin2x+cos2x=cos4x+sin2x1=cos4x+sin2xMax=1
Now,
cos4x+sin2x=(1sin2x)2+sin2x=1+sin4x2sin2x+sin2x=sin4xsin2x+1=(sin2x12)+34Min=34
Max =1

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