Math Doubts

Compound angle formulas

Definition

An expansion of the a trigonometric function for a compound angle in terms of trigonometric functions of same angles of the compound angle is called compound angle identity.

Identities

Sine of Compound angle

$(1) \,\,\,\,$ $\sin(A+B) = \sin A \cos B + \cos A \sin B$

$(2) \,\,\,\,$ $\sin(A-B) = \sin A \cos B -\cos A \sin B$

Cosine of Compound angle

$(1) \,\,\,\,$ $\cos(A+B) = \cos A \cos B -\sin A \sin B$

$(2) \,\,\,\,$ $\cos(A-B) = \cos A \cos B + \sin A \sin B$

Tangent of Compound angle

$(1) \,\,\,\,$ $\tan (A+B) = \dfrac{\tan A + \tan B}{1-\tan A \tan B}$

$(2) \,\,\,\,$ $\tan (A-B) = \dfrac{\tan A -\tan B}{1+\tan A \tan B}$

Cotangent of Compound angle

$(1) \,\,\,\,$ $\cot (A+B) = \dfrac{\cot B \cot A -1}{\cot B + \cot A}$

$(2) \,\,\,\,$ $\cot (A-B) = \dfrac{\cot B \cot A +1}{\cot B -\cot A}$

Additional Identities

$(1) \,\,\,\,$ $\sin(A+B) \sin(A-B) = \sin^2 A -\sin^2 B \,$ (or) $\, \cos^2 B -\cos^2 A$

$(2) \,\,\,\,$ $\cos(A+B) \cos(A-B) = \cos^2 A -\sin^2 B \,$ (or) $\, \cos^2 B -\sin^2 A$



Follow us
Email subscription
Math Doubts
Math Doubts is a best place to learn mathematics and from basics to advanced scientific level for students, teachers and researchers. Know more
Follow us on Social Media
Mobile App for Android users Math Doubts Android App
Math Problems

Learn how to solve easy to difficult mathematics problems of all topics in various methods with step by step process and also maths questions for practising.

Learn more