急证:sin t + cos t - 2/[1+tan^2 (t/2) ]

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/05 14:34:24
急证:sin t + cos t - 2/[1+tan^2 (t/2) ]

急证:sin t + cos t - 2/[1+tan^2 (t/2) ]
急证:sin t + cos t - 2/[1+tan^2 (t/2) ]

急证:sin t + cos t - 2/[1+tan^2 (t/2) ]
sin t = 2tan (t/2) /[1+tan^2 (t/2) ]
cos t = [1-tan^2 (t/2) ] /[1+tan^2 (t/2) ]
以上为万能公式 ,代入知
sin t + cos t - 2/[1+tan^2 (t/2) ]

2/[1+tan^2 (t/2) ]=2cos^2 (t/2)=cos t+1
所以sin t + cos t - 2/[1+tan^2 (t/2) ]=sin t + cos t - (cos t+1)=sin t - 1<=0

2/[1+tan^2 (t/2) ]=2cos^2 (t/2)=cos t+1
所以sin t + cos t - 2/[1+tan^2 (t/2) ]=sin t + cos t - (cos t+1)=sin t - 1<=

使用万能公式就可以一步证明了:
sin t = 2tan (t/2) /[1+tan^2 (t/2) ]
cos t = [1-tan^2 (t/2) ] /[1+tan^2 (t/2) ]
以上为万能公式 ,代入知
sin t + cos t - 2/[1+tan^2 (t/2) ] <=0

原式=sin t cos t–2cos∧2(t/2)=2sin(t/2)cos(t/2) cos∧2(t/2)-sin∧2(t/2)-2cos∧2(t/2)=-【sin∧2(t/2)-2sin(t/2)cos(t/2) cos∧2(t/2)】=-【sin(t/2)-cos(t/2)】∧2≤0 应该看的懂吧,最后的形式很直接就可以看出其范围了,t取任意值都满足。

急证:sin t + cos t - 2/[1+tan^2 (t/2) ] 几何画板怎么画参数方程,不急!就是这个x=a*(2*cos(t)-cos(2*t)),y=a*(2*sin(t)-sin(2*t)) matlab中怎么对下面的程序进行二维插值并画出三维视图呢?[x,y]=meshgrid(-2:1:2);t=2;Z=[(sin(t))^3 t^2 sin(t) cos(t) (sin(t))^2;t^2 sin(t) (cos(t))^4 cos(t) (sin(t))^2;t sin(t) cos(t) t^2 (sin(t))^2;sin(t) (cos(t))^3 t^2 (sin(t))^2 求sin^2(t)*cos^4(t)dt的不定积分 -2 sin 2t / cos t 为什么等于-4sin t (sin t) / ( 1-cos t)= cos(cos(t))-cos(sin(t)) 周期怎么求 MatLab的程序问题ezplot(@(t)cos(t),@(t)sin(t),[0,2*pi]) e^(i*t^2)=cos(t^2)+i*sin(t^2)成立否? tan t/2怎么算出等于sin t /(1+cos t). x=tan(t) sin(t)-cos(t)=? Matlab程序:错误在哪里建立函数文件fun5.mfunction dy=fun5(t,y)dy=[(-5*sin(t)*(5*cos(t)-y(1))+5*cos(t)*(5*sin(t)-y(2)))*(5*cos(t)-y(1))./((5*cos(t)-y(1))^2+(5*sin(t)-y(2))^2),(-5*sin(t)*(5*cos(t)-y(1))+5*cos(t)*(5*sin(t)-y(2)))*(5*sin(t)- 如何x(t)=cos(t)+asin(t) y(t)=sin(t)+bcos(t) expressing x(t) in the form Acos(t-α)和y(t)=Bsin(t-β) ?、急在线等 matlab微分方程画图问题已知:x'[t] = 2 (Sin[t] - x[t]) /Sqrt[(Sin[t] - x[t])^2 + (Cos[t] - y[t])^2]y'[t] = 2 (Cos[t] - y[t]) /Sqrt[(Sin[t] - x[t])^2 + (Cos[t] - y[t])^2]初始x[0]=0y[0]=0画出(x,y)的轨迹 cos^3+sin^3 求化简设t=cos+sin 用matlab解二阶微分方程y''(t)= -3 cos(2t) +2sin(t)+t-3.8使用ode23或ode45 帮忙解一个常微分方程2y''(t)+y(t)=cos(3t)-sin(3t)要过程 用matlab 如何作出y与t的图?y=(sin(t)-sin(t0))^2 且 cos t+t*sin t-cos to-t0*cos t0=0