Question

tan 5° tan 25° tan 30° tan 65° tan 85° = ?

Options

• 1

• `sqrt(3)`

• `1/sqrt(3)`

• `1/2`

Answer 1

`bb(1/sqrt(3))`

Explanation:

Given expression = (tan 5° tan 85°)(tan 25° tan 65°) tan 30°

`{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)`