证明: - sin(7 theta)+ sin(5 theta)/ sin(7 theta)-sin(5 theta)=?
(sin7x + sin5x)/(sin7x-sin5x)= tan6x * cotx rarr(sin7x + sin5x)/(sin7x-sin5x)=(2sin((7x + 5x)/ 2)* cos((7x-5x)/ 2) )/(2sin((7x-5x)/ 2)* cos((7x + 5x)/ 2)=(sin6x * cosx)/(sinx * cos6x)=(tan6x)/ tanx = tan6x * cottx
什么是f(t)= sin(t / 2)+ sin((2t)/ 5)的周期?
20pi sin t - > 2pi sin期(t / 2) - > 4pi sin期((2t)/ 5) - >(10pi)/ 2 = 5pi 4pi和5pi的最小倍数 - > 20 pi常见时期f(t) - > 20pi
你如何证明1 /(1 + sin(theta))+ 1 /(1-sin(theta))= 2sec ^ 2(theta)?
见下图LHS =左手边,RHS =右手边LHS = 1 /(1 + sin theta)+ 1 /(1-sin theta)=(1-sin theta + 1 + sin theta)/((1 + sin) theta)(1-sin theta)) - >公分母=(1-cancelsin theta + 1 + cancelsin theta)/((1 + sin theta)(1-sin theta))= 2 /(1-sin ^ 2x) = 2 / cos ^ 2x = 2 * 1 / cos ^ 2x = 2sec ^ 2x = RHS