Question

if tanA+cotA= 4/√3 than sinA+cosA=?

Answer 1

I proved steps are correct. any way check it in my mind sent it is crt

Answer 2

$tan \alpha + \cot \alpha = \frac{4}{ \sqrt{3} } \\ \\ tan \alpha + \frac{1}{tan \alpha } = \frac{4}{ \sqrt{3} } \\ \\ \frac{sin \alpha }{ \cos \alpha } + \frac{cos \alpha }{ \sin \alpha } = \frac{4}{ \sqrt{3} } \\ \\ \frac{1}{sin \alpha .cos \alpha } = \frac{4}{ \sqrt{3} } \\ \\ sin \alpha .cos \alpha = \ \frac{ \sqrt{3} }{4} \\ \\ let \: sin \alpha + cos \alpha = x \\ \\ {x}^{2} = {sin}^{2} \alpha + {cos}^{2} \alpha = 2sin \alpha .cos \alpha \\ \\ {x}^{2} = 1 + \frac{ \sqrt{3} }{2} \\ \\ x = \sqrt{ \frac{2 + \sqrt{3} }{2} }$