tan 5° tan 25° tan 30° tan 65° tan 85° = ?
(a) √3
(b) 1√3
(c) 1
(d) none of these
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Correct answer = (b) 1/√3
We have
tan 5° tan 25° tan 30° tan 65° tan 85°
= tan 5° tan 25° tan 30° tan(90° − 25°) tan(90° − 5°)
= tan 5° tan 25° × 1/√3 × cot 25° cot 5° [∵ tan(90° − θ) = cot θ and tan 30° = 1/√3 ]
= 1/√3