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Evaluate: ` (cos 58^@)/(sin 32^@)+(sin 22^@)/(cos 68^@)-(cos 38^@cosec 52^@)/(tan 18^@tan 35 ^@ tan 60^@tan 72^@tan 55^@)`.

Answer» Given expression
` (cos 58^@)/(sin 32^@)+(sin 22^@)/(cos 68^@)-(cos 38^@cosec 52^@)/(tan 18^@tan 35 ^@ tan 60^@tan 72^@tan 55^@)`.
` =(cos 58^@)/(sin(90^@-58^@))+(sin 22^@)/(cos (90^@-22^@))-(cos 38^@cosec(90^@-38^@))/((tan 18^@tan 72^@)(tan 35^@tan 55^@)tan 60^@)`
` =(cos 58^@)/(cos 58^@)+(sin 22^@)/(sin 22^@)`
` -(cos 38^@sec 38^@)/({tan 18^@tan(90^@-18^@)}{tan 35^@-tan(90^@-35^@)}tan 60^@)`
`=(1+1)-(1)/((tan 18^@cot 18^@)(tan 35^@cot 35^@)sqrt(3))`
` =(2-(1)/(sqrt(3)))=(2sqrt(3)-1)/(sqrt(3))=(2sqrt(3)-1)/(sqrt(3))xx (sqrt(3))/(sqrt(3))=(1)/(3)(6-sqrt(3))`.


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