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k2-1k2 +1lfcosec θ + cot θk then prove that cos θ |
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Answer» Given that cosec x +cot x = k --------------(1)we know thatcosec^2x -cot^2 x = 1(cosec x +cot x)(cosec x -cot x) = 1k (cosec x-cot x) = 1(cosec x-cot x) = 1/k ------------------(2) from (1) &(2)cosec x+cot x = kcosec x-cot x = 1/k 2cosec x = k+1/k2cosec x= k^2+1/kcosec x = k^2+1/2ksin x = 2k/k^2+1we know thatcosx =√1-sin^2 xcos x =√1-[2k/k^2+1]^2cos x =√1-4k^2/(k^2+1)^2cos x =√(k^2+1)^2-4k^2/(k^2+1)^2cos x =√(k^2-1)^2/(k^2+1)^2 {·(a+b)^2-(a-b)^2 = 4ab}cos x =√[k^2-1/k^2+1]^2cos x = k^2-1/k^2+1 Hence proved Thank you but can you send another simple method |
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