Practice your tangent sum and difference formula!

Geometry Level 2

If tanA=12 \tan A = \frac 1 2 and tanB=13 \tan B = \frac 1 3 , find the values of tan(2A+B) \tan(2A+B) and tan(2AB) \tan (2A- B) respectively.

Details and Assumptions:

  • The choices depicts the two values: tan(2A+B) \tan(2A +B) and tan(2AB) \tan(2A-B) in that order.

Bonus: If we know that only one of the choices given is definitely correct, determine which one of it is correct without manually computing any of the two values in question.

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