If cot43θ + tan43θ = 2, find 2sin2θ + cos4θ.

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

Now,

⇒ 2sin²θ + cos⁴θ = 2 × (\(\frac{1}{\sqrt {2}}\))² + (\(\frac{1}{\sqrt {2}}\))⁴ 

= 2 × \(\frac{1}{2}\) + \(\frac{1}{4}\) = 1 + \(\frac{1}{4}\) = \(\frac{5}{4}\)