Find the exact value of the expression tan 250 tan 1100 1

Find the exact value of the expression:

tan 25⁰ + tan 110⁰ / 1 - tan 25⁰tan 110⁰

Solution

(tan 25⁰ + tan 110⁰) / (1 - tan 25⁰tan 110⁰⁾

Use the tan formula : tan(A+B) = [ tanA + tanB]/( 1 -tanAtanB)

(tan 25⁰ + tan 110⁰) / (1 - tan 25⁰tan 110⁰⁾

= tan(25+110) = tan(135) = tan(90+45) = cot45 = 1