simplify sin(A+B)-sin(A-B)
Answers
Answer:
2 Cos A sin B
Step-by-step explanation:
sin A cos B+ cos A sin B -(sin A cos B - cos A sin B)
=2 Cos A sinB
Concept:
The trigonometric formula for sin(A + B) is given as sinA.cosB + cosA.sinB and for sin(A - B) is given as sinA.cosB - cosA.sinB.
Given:
An expression is given as sin(A + B) - sin(A - B).
Find:
The simplified value of the given expression is to be found.
Solution:
The value of the expression can be found by putting both formulas in the expression.
The formulas are:
sin(A + B) = sinA.cosB + cosA.sinB
sin(A - B) = sinA.cosB - cosA.sinB
Put the values in the given expression:
sin(A + B) - sin(A - B)
= sinA.cosB + cosA.sinB - (sinA.cosB - cosA.sinB)
= sinA.cosB + cosA.sinB - sinA.cosB + cosA.sinB
= sinA.cosB - sinA.cosB + cosA.sinB + cosA.sinB
= 2cosA.sinB
Hence, the value of sin(A+B)-sin(A-B) after simplifying is 2cosA.sinB.
#SPJ3