sin(α)cos(β) + sin(β)cos(α)
1
The expression sin(α)cos(β) + sin(β)cos(α) is known as the sine of the sum of two angles identity. We can use the following steps to simplify the expression:
Step 1: Use the angle addition formula for sine
sin(α + β) = sin α cos β + cos α sin β
Step 2: Rewrite the expression sin(α)cos(β) + sin(β)cos(α) in terms of sin(α + β)
sin(α)cos(β) + sin(β)cos(α) = sin α cos β + cos α sin β
Step 3: This means that sin(α)cos(β) + sin(β)cos(α) is equal to sin(α + β).
Therefore, sin(α)cos(β) + sin(β)cos(α) = sin(α + β).
Hence, the expression can be simplified to the sine of the sum of the two angles α and β.
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