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यदि \( \sin \theta+\operatorname{cosec} \theta=2 \), तो \( \sin ^{10} \theta+\operatorname{cosec}^{10} \theta \) का मान होगा |
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Answer» Solution: Given, sin θ + cosec θ = 2 sin θ + (1/sin θ) – 2 = 0 sin2θ + 1 – 2 sin θ = 0 (sin θ – 1)2 = 0 sin θ – 1 = 0 sin θ = 1 cosec θ = 1/sin θ = 1 sin10θ + cosec10θ = (1)10 + (1)10 = 1 + 1 = 2 sin θ + cosec θ = 2 = sin θ + \(\cfrac1{sin\,θ}\) = 2 sin2 θ + 1 = 2 sin θ = sin2 θ - 2sin θ + 1 = 0 = (sin θ - 1)2 = 0 = sin θ - 1 = 0 = sin θ = 1 \(\therefore\) cosec θ = \(\cfrac1{sin\,θ}\) = \(\cfrac1{1}\) = 1 sin10 θ + cosec10 θ = 110 + 110 = 1 + 1 = 2 |
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