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Prove that tan 7°. tan 23°. tan60°. tan 67°. tan83° = √3.

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Prove that tan 7°. tan 23°. tan60°. tan 67°. tan83° = √3.
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Taking LHS = tan 7° tan 23° tan 60° tan 67° tan 83° 

= cot(90° - 7°) tan (90° - 23°) tan 60° tan 67° tan 83° [∵ tan θ = cot (90° - θ)] 

= cot 83° cot 67° tan 60° tan 67° tan 83°

= tan 60° [∵ tan 60° =√3] 

= √3 = RHS

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