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Prove that : tan9°. tan27°. tan45°. tan63°. tan81° = 1

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Prove that :  tan9°. tan27°. tan45°. tan63°. tan81° = 1

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Taking LHS

= tan 9° tan 27° tan 45° tan 63° tan 81°

= cot(90° - 9°) tan (90° - 27°) tan 45° tan 63° tan 81° [∵ tan θ = cot (90° - θ)]

= cot 81° cot 63° tan 45° tan 63° tan 81°

= tan 45° [∵ tan 45° =1]

=1 = RHS

Hence Proved

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