How to determine whether two complex trig equation is identical.

by PrudensOptimus
Tags: complex, determine, equation, identical, trig
 P: 640 I believe, many of us had this problem: After finding the integral of some function, we wonder, what the right answer would be. So we goto http://integrals.wolfram.com to look up the answer. The answer the "Integral machine" gave is not always in the same form our answers are. For example: ∫ Cos[x]^3 = u - u^3/3, where u = sin x. The answer the integral machine outputs would be something more nastier... Can someone explain, how do you generally determine whether an expression is identical to another expression(usually in a more complex form)?
 Emeritus Sci Advisor PF Gold P: 5,533 I don't know of a general method, but you can handle trigonometric cases by using the relevant identities. For instance, in the example you cited you have: ∫cos3(x)dx=sin(x)-(1/3)sin3(x)+C Wolfram's "Integral Machine" gave this answer: ∫cos3(x}dx=(3/4)sin(x)+(1/12)sin(3x)+C (note, in both cases I added the "+C" in myself). The obvious difficulty in comparing the above antiderivatives is in the "3x" argument in the second one. You need to use an identity that reduces the argument to "x" in every term. The identity is: sin3(x)=(3/4)sin(x)-(1/4)sin(3x)
 P: 640 isn't Sin3x also ((1-cos2x)/2)*sinx?
Emeritus