Multiple angle formulas

sin 5A=5 sinA−20 sin^3 A+ 16 sin^5 A

cos 5A=16 cos^5 A−20 cos^3 A+ 5 cosA

tan 5A=tan

(^5) A−10 tan (^3) A+ 5 tanA
1 −10 tan^2 A+ 5 tan^4 A
sin 6A=6 cos^5 AsinA−20 cos^3 Asin^3 A+ 6 cosAsin^5 A
cos 6A= cos^6 A−15 cos^4 Asin^2 A+ 15 cos^2 Asin^4 A−sin^6 A
tan 6A= 6 tanA−20 tan
(^3) A+ 6 tan (^5) A
1 −15 tan^2 A+ 15 tan^4 A−tan^6 A
Summation and difference formula
sinA+ sinB=2 sin(
A+B
2 ) cos(
A−B
2 ),
cosA+ cosB=2 cos(A+B
2
) cos(A−B
2
),
tanA+ tanB=sin(A+B)
cosAcosB
,
sinA−sinB=2 sin(
A−B
2 ) cos(
A+B
2 )
cosA−cosB=−2 sin(A−B
2
) sin(A+B
2
)
tanA−tanB=sin(A−B)
cosAcosB
Product formula
sinAsinB=
1
2
cos(A−B)−
1
2
cos(A+B)
cosAcosB=^1
2
cos(A−B) +^1
2
cos(A+B)
sinAcosB=
1
2 sin(A−B) +
1
2 sin(A+B)
Additional relations
sin(A+B) sin(A−B) = sin^2 A−sin^2 B,
−sin(A+B) sin(A−B) = cos^2 A−cos^2 B,
cos(A+B) cos(A−B) = cos^2 A−sin^2 B,
sinA±sinB
cosA+ cosB = tan(
A±B
2 )
sinA±sinB
cosA−cosB =−cot(
A∓B
2 )
sinA+ sinB
sinA−sinB

tan(A+B
2
)
tan(
A−B
2 )