用四则运算法则验证下列导数公式:(1)(cotx)′=-csc2x;(2)(secx)′=secxtanx. A. 不变 B. 变长 C. 变短
【解析】(1 (cotx)^f=((cosx)/(sinx))'=(-sin^2x-cos^2x)/(sin^2x)=-1/(sin^2x)=-c8c^2x 2)(secx)^t=(1/(cosx))'=(sinx)/(cos^2x) =1/(cosx)⋅(sinx)/(cosx)=secxtanx【导数的运算】基本初等函数的导数公式:(1)(为常数),则;((E;(E若f(z)=sinz;(若f()=cos;(5)若...
=∫(sinx/sin^2x)dx=∫[1/(1-cos^2x)]*[-d(cosx)]=-∫[1/(1+cosx)(1-cosx)]dcosx=-1/2∫[(1+cosx+1-cosx)/(1+cosx)(1-cosx)]dcosx=-1/2∫[1/(1-cosx)+1/(1+cosx)]dcosx=-1/2∫{[1/(1-cosx)]d(1-cosx)+[1/(1+cosx)]d(1+cosx)}=-1/2∫(ln l 1-cosx l+ln...
csc^2x-1 =1/sin^2x-1 =(1-sin^2x)/sin^2x =cos^2x/sin^2x =cot^2x
两边乘以sin^4 x sin^4 x-2sin^x=cos^4 x-1 sin^4 x-cos^4 x=2sin^x-1 sin^x -cos^x=-cos2x ∴ 1-2csc^x=cot^4x-csc^4x
解析 =: -sin rsin x- cos xcos x sin2x+ cos2 x 9. (1) (cotx)'=((cosx)/(sinx))'=(-sinxsinx-cosx)/(sin^2x)⋅cosx)=-(sin^2x+cos^2x)/(sin^2x)=-1/(sin^( sin2x sin2x sin escfur, (2) (cscx)'=(1/(sinx))'=-(cosx)/(sin^2x)=-cscxcotx e rtx. ...
用四则运算法则验证下列导数公式:(1)(cotx)′=-csc2x;(2)(secx)′=secxtanx. 答案 【解答】解:(1)(cotx)′=(cosxsinx)′=-sin2x-cos2xsin2x=-1sin2x=-csc2x.(2)(secx)′=(1cosx)′=sinxcos2x=1cosx•sinxcosx=secxtanx.【分析】使用导数的运算法则进行验证. 结果二 题目 用四则运算法则验证...
Prove that : tanx + cotx = 2sec(2x) Solve tan(x) - cot(x) = 0 How do you verify sin(x) + cos(x) cot(x) = csc(x)? Verify the following identity: csc(x) - cos(x) \: cot(x) = sin(x). How does ((csc^2(x)-1)/csc^2(x))^(1/2) equal on of these: sec(x)...
Simplify the trigonometric expression: (sin^2x)^{3/2}. Use the fundamental trigonometric identities to simplify the expression. sin(theta)csc(-theta)tan(-theta) Use the fundamental trigonometric identities to simplify the expression. {1 \over {\cot }^2}x + 1 Use the fundamental trig...
方法如下，请作参考：这里