মান নির্ণয় করো : \(\cfrac{2}{3}cosec^258^\circ-\cfrac{2}{3}cot58^\circ.tan32^\circ-\cfrac{5}{3}tan13^\circ\) \(.tan37^\circ.tan45^\circ.tan53^\circ.tan77^\circ\)
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\(\cfrac{2}{3}cosec^258^\circ-\cfrac{2}{3}cot58^\circ.tan32^\circ-\cfrac{5}{3}tan13^\circ\) \(.tan37^\circ.tan45^\circ.tan53^\circ.tan77^\circ\)
\(=\cfrac{2}{3}cosec^258^\circ-\cfrac{2}{3}cot58^\circ.tan(90^o-58^o)-\cfrac{5}{3}tan13^\circ\) \(.tan37^\circ.tan45^\circ.tan(90^o-37^o).tan(90^o-13^o)\)
\(=\cfrac{2}{3}cosec^258^\circ-\cfrac{2}{3}cot58^\circ.cot58^\circ -\cfrac{5}{3}tan13^\circ\) \(.tan37^\circ.tan45^\circ. cot 37^o.cot 13^o\)
\(=\cfrac{2}{3}\left[cosec^258^\circ-cot^258^\circ\right] -\cfrac{5}{3}\cancel{tan13^\circ}\) \(.\cancel{tan37^\circ}.1. \cfrac{1}{\cancel{tan 37^o}}.\cfrac{1}{\cancel{tan 13^o}}\)
\(=\cfrac{2}{3}\times 1 -\cfrac{5}{3}\)
\(=\cfrac{2}{3}-\cfrac{5}{3}\)
\(=\cfrac{2-5}{3}\)
\(=\cfrac{-3}{3}\)
\(=-1\) [Answer]
