Write the Given Formulae: Sin C + Sin D =

Write the given formulae: Sin C + Sin D = ? SinC – Sin D = ? Cos C + Cos D = ? Cos C – Cos D = ?

Formula for 

1. Sin C + Sin D= 2 Sin (C+D/2) Cos (C-D/2) 

So first, you have to calculate the value of C+D and divide it by 2. Say the answer is x. So you will find sin x. Then find C-D and divide by 2. Say the answer is y. So we’ll find the value of Cos y. 

Then multiply Sin x and Cosine y by two and you will get the answer. 

Example: Let C= 90 and D=40

Sin C+ Sin D= 2 Sin (90+40/2) Cos (90-40/2)

2 Sin 130/2 Cos 50/2 

Ans is 2 Sin 65 Cos 25 

2. SinC – Sin D = 2 cos [(C + D) / 2] sin [(C – D) / 2]

In case there is a subtraction sign, in between the order of Sin and Cos will reverse. So first you will calculate the sum of C+D and divide it by 2. Then calculate the Cosine of the value obtained. Similarly, subtract C and D and divide it by 2. Then find the sin value of the difference obtained. 

Multiply both the values with 2 and you will get the answer. 

3. Cos C + Cos D = 2 cos [(C + D) / 2] cos [(C – D) / 2]

In case of cos, we have to obtain the sum and difference of C & D and divide by 2. But here instead of deriving the sine value we’ll obtain the cosine value of both sum and difference. Then multiply the cosine values with 2. 

4. Cos C – Cos D = – 2 sin [(C + D) / 2] sin [(C – D) / 2]

In the case of the subtraction sign between cosine C and cosine D, we’ll obtain the value of sine of sum and difference. Also, Unlike the previous three where we multiply the value with positive 2, here we will multiply with negative 2.