Question

`((cos 38^circ "cosec"  52^circ)/(tan 18^circ tan 35^circ tan 60^circ tan 72^circ tan 55^circ))` = ?

Options

• `1/3`

• `1/sqrt(3)`

• `sqrt(3)`

• `2/sqrt(3)`

Answer 1

`bb(1/sqrt(3))`

Explanation:

Given expression = `{(cos 38^circ "cosec" (90^circ - 38^circ))/((tan 18^circ tan 72^circ)(tan 35^circ tan 55^circ)tan 60^circ)}`

= `(cos 38^circ sec 38^circ)/({tan 18^circ tan (90^circ - 18^circ)}{tan 35^circ tan(90^circ - 35^circ)} xx sqrt(3))`

= `1/((tan 18^circ cot 18^circ)(tan 35^circ cot 35^circ) xx sqrt(3))`

= `1/sqrt(3)`