Question

prove that
1.tan 9° tan 27tan 45° tan 63° tan 81° = 1​

Answer 1

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.