Is there a faster, effective way to remember trigonometric identities? Esp. the Product to Sum and Sum to Product identities? I've heard about methods like derivation, but I don't know how to do that. Any tips, or advice would be extremely helpful. Thank You!
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Remember the rules of logarithms: the sum of the logarithms having the same base becomes the logarithm of the product of the numbers.
sin x + sin y = `2 sin (x+y)/2 *cos(x-y)/2`
sin x - sin y = `2 cos(x+y)/2 *sin(x-y)/2`
Use the notation `(x+y)/2 =alpha =gt x+y = 2 alpha`
`(x-y)/2 = beta =gt x-y = 2 beta`
Adding the equations yields: `2x = 2(alpha + beta) =gt x = alpha + beta`
Subtract x-y from x+y => `2y = 2(alpha + beta) =gt y = alpha - beta`
`sin (alpha + beta) + sin (alpha- beta) = sin alpha*cos beta + sin beta*cos alpha + sin alpha*cos beta - sin beta*cos alpha`
Reducing the opposite terms yields:
`sin (alpha + beta) + sin (alpha- beta) = 2 sin alpha*cos beta`