Question

simplify sin(A+B)-sin(A-B)​

Answer 1

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

Answer 2

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.

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