A blend of trigonometry and logarithms

Geometry Level 2

e log ⁡ 10 tan ⁡ 1 ∘ × e log ⁡ 10 tan ⁡ 2 ∘ × … × e log ⁡ 10 tan ⁡ 8 9 ∘ { e }^{ \log _{ 10 }{ \tan 1^\circ } }\times { e }^{ \log _{ 10 }{ \tan 2^\circ } } \times \ldots \times { e }^{ \log _{ 10 }{ \tan 89^\circ } }


The answer is 1.

Bala Vidyadharan by Bala vidyadharan , 20, India

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1 solution

Kay Xspre
Aug 1, 2015

e l o g 10 ∏ n = 1 89 t a n ( n ∘ ) e^{log_{10}\prod_{n=1}^{89}tan(n^{\circ})} = e l o g 10 ∏ n = 1 44 t a n ( n ∘ ) ∏ n = 1 44 c o t ( n ∘ ) t a n ( 4 5 ∘ ) = e^{log_{10}\prod_{n=1}^{44}tan(n^{\circ})\prod_{n=1}^{44}cot(n^{\circ})tan(45^{\circ})} = e l o g 10 1 =e^{log_{10}1} From here it will be e 0 = 1 e^0 = 1

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