How to prove equations using double-angle identities

There are so many different kinds of trigonometric identities; double-angle identities are just one kind. Their purpose is to take the "double angle" inside a trig function, and transform the expression into a "regular" angle.

Oftentimes, we'll be asked to prove an equation using trig identities. In that case, our goal is to show that the left side of the equation is the same as the right side of the equation. Trig identities allow us to manipulate and rewrite each side of the equation in different ways (without changing the actual value of the equation), until we get to a point where we can see that the sides are in fact equal to one another.

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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)

Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”

[Nameci-woht]

One could also prove it in less "tedious" way: 4sinxcos^3x - 4sin^3xcosx = 2(2sinxcosx(cos^2x-sin^2x)) = 2sin2xcos2x = sin4x

[ekkyrufendhika]

Keep up the good works you're calculus videos are help most of university student

[stephberrie]

this has nothing to do with this topic but i'm desperate. so if z=f(x, y) with no z given as you can see and a given x and y equation and they ask you to find the second partial derivative d^2z/dr^2, is it necessary to do product rule???

[muhammadhamzajaved]

Impressive video . Haha i remember these topics of Trigonometry ! How i used to find ways to prove the equation using single, double and triple trigonometric equations .Ha the feeling of nostalgia is soothing .