Welcome 2016! Part 4

Geometry Level 3

$\large \cot(10^{\circ}) \times \cot(30^{\circ}) \times \cot(50^{\circ}) \times \cot(70^{\circ}) = \ ?$

Find the value of above expression.

Image Credit: Wikimedia John Redden .

The answer is 3.

1 solution

Akhil Bansal
Dec 11, 2015

$\dfrac{\cot(30°)}{\tan(\color{#3D99F6}{10°}) \times \tan (50°) \times \tan (70°)}$ Using trigonometric identity, $\tan(\color{#3D99F6}{\theta})\cdot \tan(60-\color{#3D99F6}{\theta})\cdot \tan(60+\color{#3D99F6}{\theta}) = \tan(3\color{#3D99F6}{\theta})$ $\dfrac{\cot(30°)}{\tan(30°)} = \cot^2(30°) = 3$

Moderator note:

Good approach. That tangent "triple angle identity" is often used.

Did exactly the same!

Ganesh Ayyappan - 5 years, 6 months ago

Wow, What a coincidence. Right ?

Arian Tashakkor - 5 years, 6 months ago

@Ganesh Ayyappan @arian tashakkor Please refrain from typing in all caps, as that is considered very rude on the internet. Thanks for your assistance!

Calvin Lin Staff - 5 years, 5 months ago

@Calvin Lin – ok sir ... didnt know till this moment of my life that All Caps meant rudeness

@Arian Tashakkor ... i dont think its coincidence .... maybe thats an obvious method every math lover who wants to do sums in short and sweet manner goes for ....

Ganesh Ayyappan - 5 years, 5 months ago

@Ganesh Ayyappan – Thanks! No worries, just building a better community :)

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