tan $5^\circ$ tan $25^\circ$ tan $30^\circ$ tan $65^\circ$ tan $85^\circ$ = ?

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KollegeApply · Accepted Answer

bb(1/sqrt(3)) Explanation: Given expression = (tan $5^\circ$ tan $85^\circ$)(tan $25^\circ$ tan $65^\circ$) tan $30^\circ$ `{tan 5^circ tan (90^circ - 5^circ)}{tan 25^circ tan (90^circ - 25^circ)} xx 1/sqrt(3) ...[∵ tan 30^circ = 1/sqrt(3)] = (tan 5^circ cot 5^circ)(tan 25^circ cot 25^circ) xx 1/sqrt(3) = 1 xx 1 xx 1/sqrt(3) = 1/sqrt(3)`

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