Trigonometry is one of the most important topics in maths and physics. Trigonometry is the division of maths, which is essentially about angles and measurement. The functions that come under trigonometry are made up of compound angles, multiple angles, and trigonometric ratios. These functions are implemented for finding accurate results. Here we will discuss trigonometric ratios of the compound angles along with some of the questions and their answers.
An angle can be defined as the ray that has its rotation around the startup point. The point where rotation starts is initial and the point where it tends to stop is the final one. When the ray is rotated in the anticlockwise direction, it will create a positive angle. However, rotation of the ray in clockwise direction will have a negative angle. The angle can be measured either in the degrees or radians.
What are Compound Angles?
The compound angle can be defined as an algebraic sum of two or more than two angles. The compound angles represent various trigonometric identities. Here is the complete list of the trigonometric ratios for compound angles.
1) cos A cos B – sin A cos B = cos (A + B)
2) cos A cos B + sin A cos B equals to cos (A – B)
3) sin A cos B + cos A sin B equals to sin (A + B)
4) sin A cos B – cos A sin B = sin (A – B)
5) Sin2 A - Sin2 B= sin (A + B) sin (A – B) = cos2B - cos2 A
6) cos2 A – Sin2 A - Sin2 B = cos (A + B) cos (A – B) = cos2B - Sin2 A
7) tanA + tanB / 1 - tanAtanB = tan (A+B
8) tanA - tanB / 1 + tanAtanB = tan (A - B)
Similarly you can find for the difference or sum of the sines and cosines, multiples, for the sub-multiple and multiple angles, trigonometric ratios of the multiples of an angle by referring to the Vedantu notes on “Trigonometric ratios of compound angles”. You can also refer to several problems with solutions that use compound angle formulae.
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