Question

If tanα+cotα=2 then
√tanα+√cotα=.........

Answer 1

$\bf HELLO\: \: DEAR, \\ \\ \bf\:given \:\:that :- tan\alpha + cot \alpha = 2 \\ \\ \bf\: \: sin\alpha / cos\alpha + cos\alpha / sin\alpha = 2 \\ \\ \bf (sin^{2}\alpha + cos^{2}\alpha) / sin\alpha * cos\alpha = 2 \\ \\ \bf 1 = 2sin\alpha * cos\alpha \\ \\\bf 1 = sin2\alpha \\ \\ \bf sin2\alpha = sin90 \\ \\ \bf 2\alpha = 90 \\ \\ \bf \alpha = 45$


$\bf now, \\ \\ \bf \sqrt{tan\alpha} + \sqrt{cot\alpha} \\ \\ \bf \: \:\sqrt{tan45} + \sqrt{cot45} \\ \\ \bf ( 1 + 1) = 2 \\ \\ \bf I \:\:HOPE \:\:ITS\:\: HELP\:\: YOU \:\:DEAR, \\ \bf THANKS$