Angles A and B satisfy A + B = 45^°, and it follows that tan A + tan B + tan Atan B = 1. By putting A = B = 22tfrac12^° and writing t = tan 22tfrac12^°, write down the resulting quadratic equation in t.

Angles $A$ and $B$ satisfy $A + B = 45^\circ$ , and it follows that $\tan A + \tan B + \tan A\tan B = 1$ . By putting $A = B = 22\tfrac12^\circ$ and writing $t = \tan 22\tfrac12^\circ$ , write down the resulting quadratic equation in $t$ .

Model answer

t^2 + 2t - 1 = 0

Also accepted: t^2+2t-1=0, 2t + t^2 = 1, t^2 + 2t = 1

Explanation

Putting

A=B=22\tfrac12^\circ

\tan A+\tan B+\tan A\tan B=1

gives

t+t+t^2=1

, that is

t^2+2t-1=0

Derived from ZIMSEC Mathematics Paper 2, November 2010, Q1

Danho has every sitting for this paper, with your progress tracked question by question, offline.