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Find the maximum value of 4sin^2x+3cos^2...

Find the maximum value of `4sin^2x+3cos^2+sinx/2+cosx/2dot`

Text Solution

Verified by Experts

We have
`S=4sin^(2)x+3cos^(2)x+sin""(x)/(2)+cos""(x)/(2)`
`=3+sin^(2)x+sin""(x)/(2)+cos""(x)/(2)`
`=3+sin^(2)x+sqrt(2)sin((pi)/(4)+(x)/(2))`
Clearly, maximum value of S occurs when `x=(pi)/(2)`.
So, `S_("max")=3+1+sqrt(2)=4+sqrt(2)`
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