ext/static/chunks/a3334c652b046c3c.js","/_next/static/chunks/81b954b7224a589b.js","/_next/static/chunks/5a05ab8ee13b0bc4.js","/_next/static/chunks/6a6cb77c3f1aa625.js","/_next/static/chunks/32fdb7a303638b44.js","/_next/static/chunks/3be0177d875a105f.js","/_next/static/chunks/03e5fc0c4e7453d7.js","/_next/static/chunks/5c76b79364f9765a.js","/_next/static/chunks/718b487edc6243e6.js","/_next/static/chunks/f4c85fceb03175a8.js","/_next/static/chunks/1d422ca4614fbd39.js","/_next/static/chunks/84af6b765e7bcd95.js","/_next/static/chunks/91c05db7234c690f.js"],""] 23:I[605500,["/_next/static/chunks/18e2520e95b8024c.js","/_next/static/chunks/09dfb6945efb942a.js","/_next/static/chunks/c87c7a10fa5002a5.js","/_next/static/chunks/62b540b0ec1fd623.js","/_next/static/chunks/397198a845d2c3dc.js","/_next/static/chunks/99745078d480a4ae.js","/_next/static/chunks/fdc5802a61eabbac.js","/_next/static/chunks/7bebe4ee53854e8e.js","/_next/static/chunks/a3334c652b046c3c.js","/_next/static/chunks/81b954b7224a589b.js","/_next/static/chunks/5a05ab8ee13b0bc4.js","/_next/static/chunks/6a6cb77c3f1aa625.js","/_next/static/chunks/32fdb7a303638b44.js","/_next/static/chunks/3be0177d875a105f.js","/_next/static/chunks/03e5fc0c4e7453d7.js","/_next/static/chunks/5c76b79364f9765a.js","/_next/static/chunks/718b487edc6243e6.js","/_next/static/chunks/f4c85fceb03175a8.js","/_next/static/chunks/1d422ca4614fbd39.js","/_next/static/chunks/84af6b765e7bcd95.js","/_next/static/chunks/91c05db7234c690f.js"],"Image"] 24:I[909631,["/_next/static/chunks/18e2520e95b8024c.js","/_next/static/chunks/09dfb6945efb942a.js","/_next/static/chunks/c87c7a10fa5002a5.js","/_next/static/chunks/62b540b0ec1fd623.js","/_next/static/chunks/397198a845d2c3dc.js","/_next/static/chunks/99745078d480a4ae.js","/_next/static/chunks/fdc5802a61eabbac.js","/_next/static/chunks/7bebe4ee53854e8e.js","/_next/static/chunks/a3334c652b046c3c.js","/_next/static/chunks/81b954b7224a589b.js","/_next/static/chunks/5a05ab8ee13b0bc4.js","/_next/static/chunks/6a6cb77c3f1aa625.js","/_next/static/chunks/32fdb7a303638b44.js","/_next/static/chunks/3be0177d875a105f.js","/_next/static/chunks/03e5fc0c4e7453d7.js","/_next/static/chunks/5c76b79364f9765a.js","/_next/static/chunks/718b487edc6243e6.js","/_next/static/chunks/f4c85fceb03175a8.js","/_next/static/chunks/1d422ca4614fbd39.js","/_next/static/chunks/84af6b765e7bcd95.js","/_next/static/chunks/91c05db7234c690f.js"],"QuestionCard"] 25:T62c,

এই সমস্যাটি সমাধান করতে, আমরা দ্বিগুণ কোণের সূত্র ব্যবহার করব।

ধরি, \( \theta = \tan^{-1} \frac{3}{4} \)।

তাহলে, \( \tan \theta = \frac{3}{4} \)।

আমরা জানি, সাইন-এর দ্বিগুণ কোণের সূত্রটি হলো:

\( \sin(2\theta) = \frac{2\tan\theta}{1+\tan^2\theta} \)

এখন, \( \tan\theta \) এর মান বসিয়ে পাই:

\( \sin(2\theta) = \frac{2 \times \frac{3}{4}}{1+\left(\frac{3}{4}\right)^2} \)

\( \sin(2\theta) = \frac{\frac{3}{2}}{1+\frac{9}{16}} \)

\( \sin(2\theta) = \frac{\frac{3}{2}}{\frac{16+9}{16}} \)

\( \sin(2\theta) = \frac{\frac{3}{2}}{\frac{25}{16}} \)

\( \sin(2\theta) = \frac{3}{2} \times \frac{16}{25} \)

\( \sin(2\theta) = \frac{3 \times 8}{25} \)

\( \sin(2\theta) = \frac{24}{25} \)

এখন, \( 2\theta = \sin^{-1}\left(\frac{24}{25}\right) \)

উভয় পক্ষকে 2 দ্বারা ভাগ করে পাই:

\( \theta = \frac{1}{2}\sin^{-1}\left(\frac{24}{25}\right) \)

যেহেতু \( \theta = \tan^{-1} \frac{3}{4} \) ছিল, তাই,

\( \tan^{-1} \frac{3}{4} = \frac{1}{2}\sin^{-1}\left(\frac{24}{25}\right) \)

সুতরাং, সঠিক বিকল্পটি হলো \( \frac{1}{2}\left(sin\right)^{- 1}\frac{24}{25} \)।

( tan ^ -1 3 4 ) এর মান কোনটি?