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my idea is let tan(a) is x, so we have x + 1/x = 2 square both sides above, what do you get then ...
but i think the easier way is guess directly, we knowed that the value of tan(a) and cot(a) be 1 when a = 45 or a 225 degrees, 1 + 1 = 2
now you got the answer, right ?
\[\tan A+\cot A=2,\frac{\sin A }{ \cos A }+\frac{\cos A }{ sinA }=2\] \[\frac{ \sin ^{2}A+\cos ^{2}A }{\cos A \sin A }=2\] \[1=2\sin A \cos A=\sin 2A\] \[\sin 2A=1=\sin 90,2A=90,A=45\] i think now you can solve
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