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f(x)=1+2sin x+3cos ²xf(x)=1+2sin x+ 3 (1 - sin2x)f(x) = -3sin2x + 2 sin x + 4df(x)/dx = -6sinxcosx + 2cosx = 0hence, sin x = 1/3 or cosx = 0d/dx(df(x)/dx) = -3cos2x - 2sinxIt is negative for sin x = 1/3 and positive for cos x = 0Hence, we get a maxima at x = sin-1 (1/3)Therefore, max value of f(x) is 13/3.Thanks & RegardsBharat BajajaskIITians FacultyIIT Delhi
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