Correct Answer - Option 1 : 50/21
Given:
sinθ - cosθ = 2/5
Squaring on both sides in above equation
⇒ sin2θ + cos2θ - 2 × sinθcosθ = 4/25
⇒ 1 - 2 sinθcosθ = 4/25
⇒ sinθcosθ = 21/50
Now tanθ + cotθ = \(\frac{{\sin \theta }}{{\cos \theta }} + \frac{{\cos \theta }}{{\sin \theta }}\)
⇒ \(\frac{{{{\sin }^2}\theta\ +\ {{\cos }^2}\theta }}{{\sin \theta .\cos \theta }}\)
⇒ \(\frac{1}{{\sin \theta .\cos \theta }}\)
∴ 50/21
