Q. 285.0( 2 Votes )

Prove that :

tan 9°. tan 27°. tan 45°. tan 63°. tan 81° = 1

Answer :

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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