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Question
Show that tan 7° × tan 23° × tan 60° × tan 67° × tan 83° = `sqrt(3)`.
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Solution
L.H.S. = tan 7° × tan 23° × tan 60° × tan 67° × tan 83°
= tan 7° × tan 23° × `sqrt(3)` × tan (90° – 23°) × tan (90° – 7°)
= `sqrt(3)` × [tan 7° × tan (90° – 7°)] × [tan 23° × tan (90° – 23°)]
= `sqrt(3) xx 1 xx 1` ...[∵ tan θ × tan (90° – θ) = 1]
= `sqrt(3)`
= R.H.S.
∴ tan 7° × tan 23° × tan 60° × tan 67° × tan 83° = `sqrt(3)`
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