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Prove the following identity. [sin(x+y)+sin(x-y)]/[cos(x+y)+cos(x-y)] = tan(x)

Prove the following identity. [sin(x+y)+sin(x-y)]/[cos(x+y)+cos(x-y)] = tan(x)
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5 votes
Prove the following identity.
[sin(x+y)+sin(x-y)]/[cos(x+y)+cos(x-y)] = tan(x)

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User Mmigdol
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1 Answer

3 votes

(sin(x + y) + sin(x - y))/(cos(x + y) + cos(x - y)) = tan(x)

((sin(x)cos(y) + cos(x)sin(y)) + (sin(x)cos(y) - cos(x)sin(y)))/((cos(x)cos(y) - sin(x)sin(y)) + (cos(x)cos(y) + sin(x)sin(y))) = tan(x)

((sin(x)cos(y) + sin(x)cos(y)) + (cos(x)sin(y) - cos(x)sin(y)))/((cos(x)cos(y) + cos(x)cos(y)) + (-sin(x)sin(y) + (sin(x)sin(y))) = tan(x)

(2sin(x)cos(y))/(2cos(x)cos(y)) = tan(x)

(sin(x))/(cos(x)) = tan(x)
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User Wbdarby
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