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Prove the given identity ​

Prove the given identity ​-example-1
User Khantahr
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Explanation:

tan(2x) = sin(2x)/cos(2x) = 2sinxcosx/(cos^2x - sin^2x).

Dividing the num- and denominator by sinxcosx, we get

2/(cosx/sinx - sinx/cosx) = 2/(cotx - tanx)

cotA + cotB = cosA/sinA + cosB/sinB

We just add them like fractions, with a common denominator of sinAsinB

(cosAsinB + sinAcosB)/sinAsinB

Note that sinAcosB + sinBcosA = sin(A+B)

Therefore we have

sin(A+B)/sinAsinB

User Pointerless
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