Question

Simplify the following expressions:
a.) (1/2)[sin(u+v)+sin(u-v)]
b.) (1/2)[cos(u+v)+cos(u-v)]

Answer 1

do you gave the formula for the sum of sines? (sin(a)+sin(b))

Answer 2

No.. Don't have that. Just know the law of sin and law of cosine

Answer 3

I think you need something called "Simpson's formulas" here.. And just apply it. Ever heard of it?

Answer 4

I'll look it up

Answer 5

The Prosthaphaeresis formulas, also known as Simpson's formulas, are trigonometry formulas that convert a product of functions into a sum or difference. They are given by


(1)

(2)

(3)

(4)
This form of trigonometric functions can be obtained in Mathematica using the command TrigFactor[expr].


These can be derived using the above figure (Kung 1996). From the figure, define


(5)

(6)
Then we have the identity


(7)

(8)

(9)

(10)

Trigonometric product formulas for the difference of the cosines and sines of two angles can be derived using the similar figure illustrated above (Kung 1996). With and as previously defined, the above figure gives


(11)

(12)

(13)

(14)
SEE ALSO:

Answer 6

woohoo.. but i don't see any formula..
The formula you need is: \(\sin a + \sin b = 2\sin(\frac{a+b}2)\cos(\frac{a-b}2)\).

Answer 7

It didn't paste... Thank you...

Answer 8

you should find \(\sin(u)\cos(v)\) as answer.