To determine

To Evaluate : limθ→π21−sinθ1+cos2θ

Answer

limθ→π21−sinθ1+cos2θ =14

Explanation

Calculations:

limθ→π21−sinθ1+cos2θ (00Form)Applying l'Hospital's Rule=limθ→π2−cosθ−2sin2θ(00Form )Applying l'Hospital's Rule again=limθ→π2sinθ4cos2θ=14

Conclusion: The value of the limit is limθ→π21−sinθ1+cos2θ =14