tan⁡A=pq an A = \frac{p}{q} হলে, pcos⁡2A+qsin⁡2A=? p\cos 2A + q\sin 2A = ?

Question

tan⁡A=pq 	an A = \frac{p}{q} হলে, pcos⁡2A+qsin⁡2A=? p\cos 2A + q\sin 2A = ?

Accepted Answer

ক. 3pq2−p3q2+p2 \frac{3pq^2 - p^3}{q^2 + p^2}

ব্যাখ্যা: আমরা জানি, $\cos 2A = \frac{1-	an^2 A}{1+	an^2 A} = \frac{1-(p/q)^2}{1+(p/q)^2} = \frac{q^2-p^2}{q^2+p^2}$ এবং $\sin 2A = \frac{2	an A}{1+	an^2 A} = \frac{2(p/q)}{1+(p/q)^2} = \frac{2pq}{q^2+p^2}$।
অতএব, $p\cos 2A + q\sin 2A = p\left(\frac{q^2-p^2}{q^2+p^2}ight) + q\left(\frac{2pq}{q^2+p^2}ight) = \frac{pq^2 - p^3 + 2pq^2}{q^2+p^2} = \frac{3pq^2 - p^3}{q^2+p^2}$।

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