Sum and difference formulas

In the previous post we have discussed about percent calculator and In today's session we are going to discuss about Sum and difference formulas. Whenever we deal with trigonometry we deal with the angles of trigonometric function. If we are asked to calculate the value of sin 30 then we can easily say that it is 1 /2 because it is known to us, but if we are asked to calculate the value of sin 15 or of sin 105 then we need sum and difference formulas. If we talk about sum formulas then sum formulas are:

1. sin(x + y) = sin(x)cos(y) + cos(x) sin(y),
2. cos(x + y) = cos(x)cos(y) – sin(x) sin(y), 
3. tan(x + y) = tan(x) + tan(y) / 1 – tan(x) * tan(y).

Here x and y are the two different angles.
Now if we are asked to calculate the value of sin120 , we can calculate it by sum formula as,
we can write sin 120 as sin( 60 + 60) now we will apply sin sum formula as sin60 *cos60 + cos60 *sin60 , the value of sin 60 is 3/2 and value of cos 60 is ½ so the value of sin 120 will be  √3/2 * 1/2 + 1/2 * √3/2 =  √3 /4 +  √3/4 =  √3/2. This is the required solution. (know more about Sum and difference formulas, here)
In the same way we can also calculate the value of other functions , now we will see the difference formulas,
Difference formulas:
sin(x - y) = sin(x) cos(y) - cos(x) sin(y),
cos(x - y) = cos(x) cos(y) + sin(x) sin(y),
tan(x - y) = tan(x) - tan(y) / 1 + tan(x) * tan(y).
Here x and y are the angle of triangles.
Like sum formula we can also apply difference formula  according to our need, if we are asked to calculate the value of sin 15 then we can write sin 15 as sin (45 - 30) and with the help of difference formula we can solve this problem.
If you are preparing for icse syllabus go through Box and Whisker Plots it is a important topic in mathematics.