Question

Write the given formulas


Sin C + Sin D = ?

SinC - SinD = ?

Cos C + CosD = ?

Cos C - CosD = ?

Answer 1

Hey......^_^

Here's ur ans. ⤵

✡ Sin C + Sin D = 2 sin {( C + D) ÷ 2 }× cos (C- D ) ÷ 2


.

✡ Sin C - Sin D = 2 cos { (C+D)÷2} × sin (C-D) ÷ 2


.


✡ Cos C + CosD = 2 cos {( C + D) ÷2} × cos (C-D ) ÷ 2



.


✡ Cos C - Cos D = 2 sin {(C+D) ÷ 2} × sin (D-C ) ÷ 2



_____::________

✌Hope it helps

Answer 2

Given :

SinC + SinD

SinC - SinD

CosC + CosD

CosC - CosD

To Find :

The formulas of the given trigonometric functions

Solution :

1. sinC + sinD = 2sin $\frac{C+D}{2}$ cos $\frac{C-D}{2}$    
2. sinC - sinD = 2cos $\frac{C+D}{2}$ sin $\frac{C-D}{2}$
3. cosC + cosD = 2cos $\frac{C+D}{2}$ cos $\frac{C-D}{2}$
4. cosC - cosD =  2sin $\frac{C +D}{2}$ sin $\frac{D-C}{2}$  

Formulas (1) and (2) transform the sum and difference of two sines into a product of a pair of sine and cosine. Formula (3) transforms the sum of two cosines into a product of two cosines and formula (4) transforms the difference of two cosines into a product of two sines.