Question

Derive the trigonometric addition formula for sine
sin(a+b)=sinacosb+cosasinb

Answer 1

Use cos(A-B) = cosAcosB + sinAsinB

Answer 2

use 90 deg transformations cos(90-A) = sinA and sin(90-A) = cos(A)

Answer 3

cos(A-B) = cosAcosB + sinAsinB
replace A with pi/2-A on both sides
cos( pi/2-A -B) = cos (pi/2-A )cosB + sin( pi/2-A )sinB
cos( pi/2-(A +B)) = sinAcosB + cosAsinB
Sin(A +B) = sinAcosB + cosAsinB

Answer 4

Why did you do the part with the 90? How does that have anything to do with the rest of the derivation?

Answer 5

@princeharryyy

Answer 6

when the transformations are done >> at 90, sin changes to cos, cos to sin, tan to cot and so on @cutiecomittee123.