Question 187 of 298MediumMCQ
If tan15∘+tan75∘1+tan105∘1+tan195∘=2a, then the value of a+a1 is: Solutions · 1
Official solution
\[\tan15^\circ = 2-\sqrt{3}, \qquad \frac1{\tan75^\circ}=\cot75^\circ = 2-\sqrt{3}\]
\[\frac1{\tan105^\circ} = \cot105^\circ = -\cot75^\circ = \sqrt{3}-2, \qquad \tan195^\circ = \tan15^\circ = 2-\sqrt{3}\]
Sum: (2−3)+(2−3)+(3−2)+(2−3)=4−23=2a⟹a=2−3.
\[\frac1a = \frac1{2-\sqrt{3}} = 2+\sqrt{3}\]
\[a+\frac1a = (2-\sqrt{3})+(2+\sqrt{3}) = 4\] Answer the question to unlock