Verified by Ajay Kumar
If cosec θ − cot θ = √2 − 1, find the value of cosec θ + cot θ.
0
√2
√2 + 2
√2 + 1
Answer: D
Solution: Use the identity \(\operatorname{cosec}^2\theta-\cot^2\theta=1\). Therefore, \((\operatorname{cosec}\theta-\cot\theta)(\operatorname{cosec}\theta+\cot\theta)=1\). Hence, \(\operatorname{cosec}\theta+\cot\theta=\frac{1}{\sqrt2-1}=\sqrt2+1\). Trick: Rationalize \(\frac{1}{\sqrt2-1}\) by multiplying numerator and denominator by \(\sqrt2+1\).
यदि cosec θ − cot θ = √2 − 1 है, तो cosec θ + cot θ का मान ज्ञात कीजिए।
0
√2
√2 + 2
√2 + 1
उत्तर: D
हल: सर्वसमिका \(\operatorname{cosec}^2\theta-\cot^2\theta=1\) का प्रयोग करें। इसलिए \((\operatorname{cosec}\theta-\cot\theta)(\operatorname{cosec}\theta+\cot\theta)=1\)। अतः \(\operatorname{cosec}\theta+\cot\theta=\frac{1}{\sqrt2-1}=\sqrt2+1\)। ट्रिक: \(\frac{1}{\sqrt2-1}\) के अंश और हर को \(\sqrt2+1\) से गुणा करके परिमेय करें।
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