When simplified, the fraction with numerator tangent of open paren 40 degrees close paren minus tangent of open paren 10 degrees close paren and denominator 1 plus tangent of open paren 40 degrees close paren times tangent of open paren 10 degrees close paren is equivalent to which expression?
Answer
A
tangent of open paren negative 50 degrees close paren
B
tangent of open paren negative 30 degrees close paren
C
tangent of open paren 30 degrees close paren
D
tangent of open paren 50 degrees close paren
Explanation
Use the tangent subtraction identity: (tan A − tan B)/(1 + tan A tan B) = tan(A − B). With A = 40° and B = 10°, the fraction becomes tan(40° − 10°) = tan 30°. Therefore, the equivalent expression is tangent of 30 degrees, choice C.
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