যদি \(\rm \frac{{(1 - \cos \theta )}}{{\sin \theta }}\) = \(\frac{1}{5}\) হয়, তবে \(\rm \frac{{(1 + \cos \theta )}}{{\sin \theta }}\) এর মান কত নির্ণয় করুন।

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Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 02 Dec 2022 Shift 4)

Answer 1

প্রদত্ত:

\(\rm \frac{{(1 - \cos θ )}}{{\sin θ }}\) = \(\frac{1}{5}\)

অনুসৃত ধারণা:

cosec²θ - cot²θ = 1

cosec2θ - cot2θ = (cosecθ + cotθ)(cosecθ - cotθ)

গণনা:

\(\rm \frac{{(1 - \cos θ )}}{{\sin θ }}\) = \(\frac{1}{5}\)

⇒ \(\rm \frac{{1}}{{\sin θ }} - \frac{cos θ}{sinθ}\) = \(\frac{1}{5}\)

⇒ cosecθ - cotθ = \(\frac{1}{5}\)

এখন,

(cosecθ + cotθ)(cosecθ - cotθ) = 1

⇒ (cosecθ + cotθ)\(\frac{1}{5}\) = 1

⇒ cosecθ + cotθ = 5

⇒ \(\rm \frac{{1}}{{\sin θ }} + \frac{cos θ}{sinθ}\) = 5

⇒ \(\rm \frac{{(1 + \cos \theta )}}{{\sin \theta }}\) = 5

∴ নির্ণেয় মান 5.

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