Find the exact value of the trigonometric expression without

Find the exact value of the trigonometric expression without the use of a calculator. StartStartFraction tangent left parenthesis StartFraction 4 pi Over 5 EndFraction right parenthesis plus tangent left parenthesis StartFraction pi Over 30 EndFraction right parenthesis OverOver 1 minus tangent left parenthesis StartFraction 4 pi Over 5 EndFraction right parenthesis tangent left parenthesis StartFraction pi Over 30 EndFraction right parenthesis EndEndFraction tan 4 5+tan 30 1tan 4 5tan 30

Solution

Let y = [Tan(4pi/5) + Tan(pi/30)]/(1 - tan(4pi/5)*tan(pi/30))

y = [Tan(144) + Tan(6)]/(1 - tan(144)*tan(6)) = [-0.7265 + 0.105]/(1 - (-0.7265*0.105)

y = -0.6215/1.0762825 = -0.57745