sin(2x) = 2sinxcosx
1
To prove this trigonometric identity, we can use the double angle formula for sine, which states that:
sin(2x) = 2sinxcosx
Step 1: Rewrite sin(2x) as sin(x+x) using the double angle formula for sine:
sin(2x) = sin(x+x) = sin(x)cos(x) + cos(x)sin(x)
Step 2: Rewrite the right-hand side of the equation using the commutative property of multiplication:
sin(x)cos(x) + cos(x)sin(x) = 2sin(x)cos(x)
Step 3: Substitute the result of step 2 into the original equation:
sin(2x) = 2sin(x)cos(x)
Therefore, we have proven that sin(2x) = 2sin(x)cos(x), using the double angle formula for sine.
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