f(x)=2sin^2(π/4+x)+根号3(sin^2x+cos^2x)f(x)=2sin^2(π/4+x)+根号3(sin^2_数学解答

f(x)=2sin^2(π/4+x)+根号3(sin^2x+cos^2x)
f(x)=2sin^2(π/4+x)+根号3(sin^2x-cos^2x) 符号打错了

人气：187 ℃　时间：2019-08-22 08:11:49

解答

f(x)=2sin^2(π/4+x)+√3(sin^2x-cos^2x)
=2sin^2(π/4+x)-√3cos2x
=1-cos(π/2+2x)+√3cos2x
=1+2(√3/2cos2x+1/2sin2x)
=1+2sin(π/3+2x)