Other trigonometric Identities (for BSEE: I - 1)

Sum and difference formulas

sin ( + β) = sin cos β + cos sin β

sin ( − β) = sin cos β − cos sin β

cos ( + β) = cos cos β − sin sin β

cos ( − β) = cos cos β + sin sin β


Double-angle formulas

sin 2A = 2 sinA cosA
cos 2A = cos^2(A)- sin^2(A)
= 2 cos^2(A)- 1
= 1 - 2 sin^2(A)

Products as sums

a) sin cos β = ½[sin ( + β) + sin ( − β)]

b) cos sin β = ½[sin ( + β) − sin ( − β)]

c) cos cos β = ½[cos ( + β) + cos ( − β)]

d) sin sin β = −½[cos ( + β) − cos ( − β)]


Sums as products

e) sin A + sin B = 2 sin ½ (A + B) cos ½ (A − B)

f) sin A − sin B = 2 sin ½ (A − B) cos ½ (A + B)

g) cos A + cos B = 2 cos ½ (A + B) cos ½ (A − B)

h) cos A − cos B = −2 sin ½ (A + B) sin ½ (A − B)