Trigonometry Identities: cos(x +/- y) = cos(x)cos(y) -/+ sin(x)sin(y)

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In this video I derive addition and subtraction identities, cos(x+y) and cos(x-y), using the Law of Cosines and the Pythagorean Theorem. This identity is very useful in all of mathematics and is used in the derivations of many trigonometric derivatives and integrals.

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  1. Math Easy Solutions
  2. trigonometry
  3. identities
  4. addition
  5. subtraction
  6. angles
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Комментарии
Автор

I don't always prove the cosine addition and subtraction identities but when I do I usually use both the law of cosines and the Pythagorean theorem in the proof ;)

mes
Автор

Hi,

Yes the proof is difficult because you need to know what Pythagoras theorem and law of cosines are.

And "c" in this proof is important because we know TWO methods of solving for it. We can then equate the two equations and solve for the cos(x-y) and get our proof.

And cos(x-y) just means you are taking the ratio of "adjacent/hypotenuse" of the angle x - y. That is all cos(x-y) is. for example. if x = 90 degrees, y = 30 degress, then you get cos(x-y)= cos(60degrees) = 1/2.

hope it helps!

mes
Автор

HI, I know this video was posted a long time ago, but I really want to know why c^2 = 1^2+1^2-2*1*1cos(x+y). because of two similar triangles?

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