数学题目已知X小于等于3л/4 x大于等于л/4,f(x)=1/2cos2x+sinx+a/4的最大值是2,求实数a的值
f(x)=(1/2)cos2x+sinx+a/4
=(1/2)[1-2(sinx)^2]+sinx+a/4
=-(sinx)^2+sinx+(a/4+1/2)
=-(sinx-1/2)^2+(a/4+3/4)
pi/4=√2/2=(√2-1)/2=(3-2√2)/4=(a+6-2√2)/4=a=4。
f(x)=(1/2)cos2x+sinx+a/4
=(1/2)[1-2(sinx)^2]+sinx+a/4
=-(sinx)^2+sinx+(a/4+1/2)
=-(sinx-1/2)^2+(a/4+3/4)
pi/4=√2/2=(√2-1)/2=(3-2√2)/4=(a+6-2√2)/4=a=4。
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