If tangent m is equal to 1 half and tangent n is equal to negative 6 , what is the exact value of tangent of open paren m plus n close paren ?

Use the tangent sum identity: tan(m + n) = (tan m + tan n) / (1 − tan m tan n). Substituting tan m = 1/2 and tan n = −6 gives (1/2 − 6) / (1 − (1/2)(−6)) = (−11/2) / 4 = −11/8. The exact value is negative 11 eighths, choice C.

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