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प्रश्न
Prove that:
`sin 18^circ/(cos 72^circ )+ sqrt(3)(tan 10^circ tan 30^circ tan 40^circ tan50^circ tan 80^circ) `
उत्तर
`"LHS" = sin 18^circ/(cos 72^circ )+ sqrt(3)(tan 10^circ tan 30^circ tan 40^circ tan50^circ tan 80^circ) `
`=(sin 18^circ)/sin(90^circ -72^circ) + sqrt(3) [cot(90^circ - 10^circ)xx1/sqrt(3)xxcot(90^circ - 40^circ )xxtan50^circ]`
`=(sin 18^circ)/(sin 18^circ) + sqrt(3) (cot 80^circxxcot 50^circ)xxtan 50^circxxtan 80^circ)/)`
`= 1 + (1/tan 80^circxx1/ tan 50^circxxtan 50^circxxtan 80^circ)`
= 2
= RHS
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