If cot55θ + tan97θ = 2, find 2sinθ + cosθ .

If cotⁿθ + tanⁿθ = 2 then cotθ = tanθ = 1 where θ = 45°

Now,

⇒ 2sinθ + cosθ = 2 × (\(\frac{1}{√2}\)) + (\(\frac{1}{√2}\)) 

= 2 × \(\frac{1}{√2}\) + \(\frac{1}{√2}\) =  \(\frac{3}{√2}\)