2024 UPDATED!!! The law of cosines is a2+b2-2abcosc=c^2 find the value of 2abcosc

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The law of cosines is a2+b2-2abcosc=c^2 find the value of 2abcosc

In this case we have the following equation:

a ^ 2 + b ^ 2-2abcosC = c ^ 2

To get the value of 2abcosC we need to follow these steps:

Subtract a ^ 2 on both sides of the equation:

$-a ^ 2 + a ^ 2 + b ^ 2-2abcosC = c ^ 2-a ^ 2 \ b ^ 2-2abcosC = c ^ 2-a ^ 2$

Subtract b ^ 2 on both sides of the equation:

$-b ^ 2 + b ^ 2-2abcosC = c ^ 2-a ^ 2-b ^ 2 \ - 2abcosC = c ^ 2-a ^ 2-b ^ 2$

Multiply both sides of the equation by -1:

$(-2abcosC) (- 1) = (c ^ 2-a ^ 2-b ^ 2) (- 1) \ 2abcosC = -c ^ 2 + a ^ 2 + b ^ 2$

the value of 2abcosC is:

2abcosC = -c ^ 2 + a ^ 2 + b ^ 2