What is the value of (sinθ+cosθ)/(sinθ-cosθ)+(sinθ-cosθ)/(sinθ+cosθ)?

\(\frac{sinθ +cosθ }{sinθ - cosθ }\) + \(\frac{sinθ -cosθ }{sinθ + cosθ }\)

= \(\frac{(sinθ +cosθ)² + (sinθ - cosθ)² }{sin²θ - cos²θ }\)

= \(\frac{(sin²θ +cos²θ +2sinθ.cosθ ) + (sin²θ + cos²θ -2sinθ.cosθ ) }{sin²θ - cos²θ }\)

{ using , sin²θ +cos²θ = 1 }

= \(\frac{2 }{sin²θ - cos²θ }\)