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Show that tan(pi/4 + theta) - tan(pi/4 - theta) = 2*tan(2*theta). Which expression equals the left-hand side?

1. 2*tan(2*theta)
2. tan(2*theta)
3. 2*tan(theta)
4. tan(pi/4)*tan(theta)

Correct answer: 2*tan(2*theta)

Solution

The difference simplifies to 4*tan theta/(1 - tan² theta) = 2*tan(2 theta).

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