যদি \(sin\theta +cosec\theta=2\) হয়, তবে \((sin^{10}\theta+cosec^{10}\theta)\) এর মান নির্ণয় করো।
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\(sin\theta +cosec\theta=2\)
বা, \(sin\theta +\cfrac{1}{sin\theta}=2\)
বা, \(\cfrac{sin^2\theta +1}{sin\theta}=2\)
বা, \(sin^2\theta +1=2sin\theta \)
বা, \(sin^2\theta +1-2sin\theta =0\)
বা, \((sin\theta -1)^2 =0\)
বা, \(sin\theta -1 =0\)
বা, \(sin\theta = 1\)
\(\therefore cosec\theta=\cfrac{1}{sin\theta}=\cfrac{1}{1}=1\)
\((sin^{10}\theta+cosec^{10}\theta)\)
\(=(1)^{10}+(1)^{10}\)
\(=1+1\)
\(=2\) [Answer]