উত্তর সিলেক্ট করলে সঠিক ও ভুল দেখাবে।
ব্যাখ্যা ও সঠিক সমাধান
উত্তর:
x²+1/x²-1
tanθ + secθ = x => (1+sinθ)/cosθ = x => (1+sinθ)²/cos²θ = x² => (1+sinθ)²/(1-sin²θ) = x² => (1+sinθ)²/((1-sinθ)(1+sinθ)) = x² => (1+sinθ)/(1-sinθ) = x². Applying componendo and dividendo: (1+sinθ+1-sinθ)/(1+sinθ-1+sinθ) = (x²+1)/(x²-1) => 2/2sinθ = (x²+1)/(x²-1) => 1/sinθ = (x²+1)/(x²-1) => cosecθ = (x²+1)/(x²-1).