what is a maxmimum value of sinx(1+cosx)
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What is the maximum value of sin x (1+cos x)?
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7 Answers

Ved Prakash Sharma, former Lecturer at Sbm Inter College, Rishikesh (1971-2007)
Answered June 25, 2018
y=sinx.(1+cosx)
dy/dx=sinx.(-sinx) +cosx.(1+cosx)
= -sin^2x+cosx+cos^2x
=-1+cos^2 x+cosx+cos^2x
=2cos^2x +cosx -1
=2cos^2x+2cosx-cosx-1
=2cosx(cosx+1)-1(cosx+1)
(cosx+1)(2cosx-1)
For maxima or minima put dy/dx=0
( cosx+1)(2cosx-1)=0
cosx+1=0 => x=180°
2cosx-1=0 =>cosx=1/2 or x=60°
dy/dx=-sin^2x+cosx+cos^2x=cosx+ cos^2x-sin^2x
dy/dx=cosx+cos2x
d2ydx^2= -sinx-2.sin2x
d2y/dx^2 (at x=180° )=0
d2y/dx^2 ( at x=60°) -ve ,there exist maxima
at x=60°.
Maximum value =sin60°(1+cos60°).
= (3^1/2)/2 (1+1/2)=(1/4).(3)^3/2 , Answer