Question

Prove that:

`sin 18^circ/(cos 72^circ )+ sqrt(3)(tan 10^circ tan 30^circ tan 40^circ  tan50^circ tan 80^circ) `

Answer 1

`"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