cos+2x-sin+2x等于多少

傅油印5090dx/(cos^2x - sin^2x) -
戚郑孟19437639026 ______ ∫dx/(cos²x-sin²x)=∫sec²xdx/(1-tan²x)=∫dtanx/(1-tan²x)=1/2∫1/(1+tanx)+1/(1-tanx)dtanx=1/2ln|(1+tanx)/(1-tanx)|+C

傅油印5090已知函数f(x)=1+cos2x - 2sin^2(x - 30°).化简 -
戚郑孟19437639026 ______[答案] f(x)=1+cos2x-2sin^2(x-30°).=cos2x+cos2(x-30)=cos2x+sin(2x+30)=cos2x+sin2xcos30+cos2xsin30=(3cos2x)/2+(√3sin2x)/2=√3(sin60cos2x+cos60sin2x)=√3sin(2x+60)

傅油印5090f(x)=cos^2x - sin^2xsin(排/2+x)的最大值为多少
戚郑孟19437639026 ______ f(x) =(cosx)^2-(sinx)^2sin(π/2+x)=(cosx)^2-(sinx)^2cosx =(cosx)^2-[1-(cosx)^2]cosx=(cosx)^3+(cosx)^2-cosx. 令cosx=t,则:f(x)=t^3+t^2-t,∴f′(t)=3t^2+2t-1=(t+1)(3t-1), f″(x)=6t+2. 令f′(x)=0,得:(t+1)(3t-1)=0,∴t=-1,或t=1/3. 显然,f″(-1)=-6+10. ∴当t=-1时,f(x)有最大值,且最大值=(-1)^3+(-1)^2-(-1)=1.

傅油印5090急!!!将f(x)=cos^2x - 2sinxcosx - sin^2x化为y=Acos(wx+φ)的形式 -
戚郑孟19437639026 ______ f(x)=(cos²x-sin²x)-sin2x =cos2x-sin2x =√2[(√2/2)cos2x-(√2/2)sin2x] =√2cos(2x+π/4)

傅油印5090证明:(1 - 2sinx·cosx)/(cos??x - sin??x)=(1 - tanx)/(1+tanx) -
戚郑孟19437639026 ______ (1-2sinx*cosx)/(cos^2x-sin^2x) =(cos^2x+sin^2x-2sinx*cosx)/(cos^2x-sin^2x) =(cosx-sinx)^2/[(cosx-sinx)*(cosx+sinx)]=(cosx-sinx)/(cosx+sinx) =(1-tanx)/(1+tanx) 证毕.

傅油印5090已知函数f(x)=cos^2x - sin^2x+2根号3sinxcosx+1,求函数f(x)的最小正周期及函数图像的对称中心;若函数X属于[0,派/2},且f(x)=2,求x的值 -
戚郑孟19437639026 ______[答案] ∵f(x)=cos��x-sin��x+2√3sinxcosx+1=cos2x+√3sin2x+1=2sin(2x+π/6)+1∴T=2π/2=π令2x+π/6=kπ,解得对称中心是(kπ/2-π/12,1)∵f(x)=2sin(2x+π/6)+1=2,则sin(2x+π/6)=1/2又∵x∈[0,π/2],则2x+π/6∈[π/6,7π/6]∴2x+π/6=π/6或5π/6解得x=0或π/3

傅油印5090求证(cos^2x - sin^2x)(cos^4x+sin^4x)+1/4sin2xsin4x=cos2x -
戚郑孟19437639026 ______[答案] 很简单,主要对1/4*sin2x*sin4x进行化简:1/4*sin2x*2*sin2x*cos2x=2sin^2x*cos^2x*cos2x; 然后右式乘以cos^2x-sin^2x化为cos2x ,提取公因式,结果一目了然了

傅油印5090怎么做出Cos(2x) - sin(2x)的图像?
戚郑孟19437639026 ______ 提根号2,化为根号2sin(2x-45)在画图

傅油印5090:求证:(cos^2x - sin^2x)(cos^4x+sin^4x)+1/4sin2xsin4x=cos2x求证:(cos^2x - sin^2x)(cos^4x+sin^4x)+1/4sin2xsin4x=cos2x我算到右边=cos2x(1 - sin^2xcos^... -
戚郑孟19437639026 ______[答案] 不知道你怎么算的 左边=cos2x[(sin²x+cos²x)²-2sin²xcos²x]+1/4sin2x*2sin2xcos2x =cos2x[1-1/2*(2sinxcosx)²]+1/2sin²2xcos2x =cos2x-1/2*sin²2xcos2x+1/2sin²2xcos2x =cos2x

傅油印5090函数y=cos²x/2 - sin²x/2的最小值 -
戚郑孟19437639026 ______ y=cos²x/2-sin²x/2 =cosx/2cosx/2-sinx/2sinx/2 =cos(x/2+x/2) =cosx ∵-1≤cosx≤1 ∴最小值为-1