Sin of sum of two angles identity is a trigonometric formula and it is one of the most useful trigonometric identities in trigonometry. It is mainly used to expand when sin function contains a compound angle (in the form of sum of two angle) as angle.

$\sin{(sum \, of \, two \, angles)}$ $\,=\,$ $\sin{(first \, angle)}\cos{(second \, angle)}$ $+$ $\cos{(first \, angle)}\sin{(second \, angle)}$

In order to avoid confusion, sine of sum of two angles formula is written in three ways internationally. You can follow one of them.

$A$ and $B$ are two angles and sum of two angles is $A+B$, then $\sin{(A+B)}$ is expanded in terms sum of product of sine and cosine of angles $A$ and $B$ as follows.

$\sin{(A+B)}$ $\,=\,$ $\sin{A}\cos{B}$ $+$ $\cos{A}\sin{B}$

$x$ and $y$ are two angles and sum of two angles is $x+y$, then $\sin{(x+y)}$ can be expanded in terms sum of product of sine and cosine of angles $x$ and $y$ in the following way.

$\sin{(x+y)}$ $\,=\,$ $\sin{x}\cos{y}$ $+$ $\cos{x}\sin{y}$

$\alpha$ and $\beta$ are two angles and sum of two angles is $\alpha+\beta$, then $\sin{(\alpha+\beta)}$ can be expanded in terms sum of product of sine and cosine of angles $\alpha$ and $\beta$ as written below.

$\sin{(\alpha+\beta)}$ $\,=\,$ $\sin{\alpha}\cos{\beta}$ $+$ $\cos{\alpha}\sin{\beta}$

List of most recently solved mathematics problems.

Jul 04, 2018

Limit (Calculus)

Evaluate $\displaystyle \large \lim_{x \,\to\, \tan^{-1}{3}} \normalsize {\dfrac{\tan^2{x}-2\tan{x}-3}{\tan^2{x}-4\tan{x}+3}}$

Jun 23, 2018

Limit (Calculus)

Evaluate $\displaystyle \large \lim_{x \to 0} \normalsize \dfrac{e^{x^2}-\cos{x}}{x^2}$

Jun 22, 2018

Integral Calculus

Evaluate $\displaystyle \int \dfrac{1+\cos{4x}}{\cot{x}-\tan{x}} dx$

Jun 21, 2018

Limit

Evaluate $\displaystyle \large \lim_{x \to \infty} \normalsize {\sqrt{x^2+x+1}-\sqrt{x^2+1}}$

Math Doubts is a best place to learn mathematics and from basics to advanced scientific level for students, teachers and researchers.
Know more

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.