Expansion of sin (A + B + C)

We will learn how to find the expansion of sin (A + B + C). By using the formula of sin (α + β) and cos (α + β) we can easily expand sin (A + B + C).

Let us recall the formula of sin (α + β) = sin α cos β + cos α sin β and cos (α + β) = cos α cos β - sin α sin β.

sin (A + B + C) = sin [( A + B) + C]

                     = sin (A + B) cos C + cos (A + B) sin C, [applying the formula of sin (α + β)]

                      = (sin A cos B + cos A sin B) cos C + (cos A cos B - sin A sin B) sin C, [applying the formula of sin (α + β) and cos (α + β)]

                       = sin A cos B cos C + sin B cos C cos A + sin C cos A cos B - sin A sin B sin C, [applying distributive property]                

                       = cos A cos B cos C (tan A + tan B + tan C - tan A tan B tan C)

Therefore, the expansion of sin (A + B + C) = cos A cos B cos C (tan A + tan B + tan C - tan A tan B tan C).











11 and 12 Grade Math

From Expansion of sin (A + B + C) to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.