2015年10月18日 · Express sin (x/2) in terms of cos x. Ans: sin (x /2) = sqrt((1 - cos x)/2) By applying the trig identity: cos 2a = 1 - 2sin^2 a, we get: cos x = 1 - 2sin^2 (x/2) 2sin^2 (x/2) = 1 …

2017年3月7日 · Calculus Differentiating Trigonometric Functions Differentiating sin(x) from First Principles. 1 Answer . Alan N.

2017年3月9日 · How do you verify the identity #sin(x/2)cos(x/2)=sinx/2#? Trigonometry Trigonometric Identities and Equations Half-Angle Identities. 1 Answer

2017年11月12日 · x^2 - x^6/(3!) + x^10/(5!) - .... sum_(n=0 )^oo x^(4n+2)/((2n+1)!) * (-1)^n First we must find the series for sin(x) let f(x) = sin(x) f(0) = sin(0) = 0 f'(0) = cos(0 ...

2016年10月30日 · #e^y=(sinx)^2# Use implicit differentiation on the left hand side of the equation and the chain rule on the right hand side of the equation: #e^y*(dy)/(dx)=2sinx*cosx#

2018年6月22日 · Note that we can write this more compactly as #csc^2x# as cosec #x# is #1/sinx#. But to take the derivative this form in terms of sin is more useful. Use the quotient …

Double Angle Identities. #sin2theta=2sin theta cos theta# #cos2theta=cos^2theta-sin^2theta=2cos^2theta-1=1-2sin^2theta#

2016年10月3日 · #(1+sinx)/(1-sinx)=(secx+tanx)^2# Right Side #=(secx+tanx)^2# #=(secx+tanx)(secx+tanx)# #=sec^2x+2secxtanx+tan^2x# ...

2016年3月8日 · This result follows almost directly from the following: (a+b)^2 = a^2+2ab + b^2 sin^2(x) + cos^2(x) = 1 sin(2x) = 2sin(x)cos(x) With these, we have (sin(x)+cos(x))^2 ...

2017年2月13日 · See explanation... Consider a right angled triangle with an internal angle theta: Then: sin theta = a/c cos theta = b/c So: sin^2 theta + cos^2 theta = a^2/c^2+b^2/c^2 = …