Matzic|

We have learned previously, trigonometric functions are depends, which means trigonometric functions such as Sine, Cosine, Tangent, Cotangent, Secant and Cosecant always depend on a variable and the variable is called as an angle. Previously, we have developed several mathematical formulas with single angle.

However, we are going to learn, trigonometric functions with different angles which sometimes called as multiple angles and sub multiple angles. These multiple and sub multiple angles’ trigonometric relationships well help us in dealing very complicated problems easily, developing more trigonometric formulas and improving knowledge on problem solving.

Most of the people do not have much knowledge on multiple and sub multiple angles functions. Now, I would like to explain multiple and sub multiple functions clearly.

Dealing one or more angles A+B, A + B + C, …. or multiple angles like 2A, 3A, ….

Dealing one ore more angles but it will be like this (A+B)/2, (A + B + C)/3, … and A/2, A/3, A/4 called as Sub multiple angles.

Actually, we mostly deal with Sine and Cosine trigonometric functions because remaining functions with multiple and sub multiple angles may not be useful in problem solving. So, we are only discussing Sine and Cosine functions with multiple angles and sub multiple angles.

Trigonometric Functions with multiple Angles

1. Sin(A + B) + Sin(A – B) = 2.SinA.CosB
2. Sin(A + B) – Sin(A – B) = 2.CosA.SinB
3. Cos(A + B) + Cos(A – B) = 2.SinA.CosB
4. Cos(A + B) – Cos(A – B) = – 2.SinA.SinB

Trigonometric functions with Sub multiple angles

1. SinC + SinD = 2.Sin[(C + D)/2].Cos[(C – D)/2]
2. SinC – SinD = 2.Cos[(C + D)/2].Sin[(C – D)/2]
3. CosC + CosD = 2.Sin[(C + D)/2].Cos[(C – D)/2]
4. CosC – CosD = – 2.Sin[(C + D)/2].Sin[(C – D)/2]

These are the mostly and commonly useful trigonometric functions with multiple and sub multiple angles. We apply these important mathematical formulas in trigonometry for easy problem solving.