Sum Formula

For any two angles A and B, we have

Difference Formula

For any two angles A and B we have

For any two angles A and B

(i) sin(A + B) sin(A - B) = sin²A - sin²B = cos²B - cos²A

(ii) cos(A + B) cos(A - B) = cos²A - sin²B = cos²B - sin²A

[The proofs of the above identities are same as for Circular functions]

Products of functions in terms of Sums and differences and

vice-versa

By adding (a) and (b) we get

Putting A + B = C and A - B = D

By subtracting (b) from (a) we get

Putting A + B = C and A - B = D

By adding (c) and (d) we get

Putting A + B = C and A - B = D

by subtracting (d) from (c) we get

Putting A + B = C and A - B = D

Summary of above results