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\(sin\theta+cos\theta =\cfrac{7}{5} ----- (i)\)
বা, \((sin\theta+cos\theta)^2 =(\cfrac{7}{5})^2\)
বা, \((sin\theta-cos\theta)^2+4 sin\theta cos\theta =\cfrac{49}{25}\)
বা, \((sin\theta-cos\theta)^2+4 \times \cfrac{12}{25} =\cfrac{49}{25}\)
বা, \((sin\theta-cos\theta)^2=\cfrac{49}{25}-\cfrac{48}{25} \)
বা, \((sin\theta-cos\theta)^2=\cfrac{1}{25} \)
বা, \(sin\theta-cos\theta=\cfrac{1}{5}-----(ii) \)

\((i)\) এবং \((ii)\) নং সমীকরন যোগ করে পাই \(sin\theta+cos\theta + sin\theta-cos\theta=\cfrac{7}{5}+\cfrac{1}{5}\)
বা, \(2 sin\theta=\cfrac{7+1}{5}\)
বা, \(sin\theta=\cfrac{\cancel8 4}{5\times \cancel2}\)
বা, \(sin\theta=\cfrac{4}{5}\) [Answer]