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Formulas of compound angels And sub multiple angels

Formulas of compound angels
And sub multiple angels
 

Grade:11

1 Answers

Harshit Singh
askIITians Faculty 5963 Points
3 years ago
Dear Student
Here is answer to your query:

Compound Angles

Angles composed of an algebraic sum or difference of two or more angles are called compound angles. Trigonometric ratios of compound angles include evaluation of trigonometric sum or trigonometric difference of two or more angles. Some of the trigonometric identities regarding the compound angles are listed below:

sin(A + B) = sinA cosB + cosA sinB

sin(A – B) = sinA cosB – cos A sin B

cos(A + B) = cosA cosB – sinA sinB


Submultiples of an Angle

As the name suggests, trigonometric ratio of a submultiple of an angle means when we try to find out some trigonometric value of an angle of the type A/2 or A/3.

Some of the trigonometric identities for the submultiple of an angle are:

(a) sin 2A = 2 sin A cos A = 2 tan A/(1+tan2A)

(b) cos 2A = cos2A – sin2A = 2cos2A-1 = 1-2 sin2A

(c) tan 2A = 2 tan A/(1-tan2A)

(d) sin 3A = 3 sinA – 4 sin3A

(e) cos 3A = 4 cos3A – 3 cos A

(f) tan 3A = (3 tan A- tan3A)/(1-tan2A)

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