Tandem progression

Geometry Level 2

tan ⁡ 5 0 ∘ tan ⁡ 6 0 ∘ tan ⁡ 7 0 ∘ = tan ⁡ N ∘ \tan 50^ \circ \tan 60^\circ \tan 70 ^ \circ = \tan N ^\circ , where 0 ≤ N < 180 0 \leq N <180 , what is the value of N N ?


The answer is 80.

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Calvin Lin by Calvin Lin

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2 solutions

Ahmad Saad
Oct 25, 2016

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Andre Yudhistika
Jan 4, 2014

i just remember it from some where that

tan30tan40tan50=tan30 ... tan50tan60tan70=tan80

tan110tan120tan130=-80... tan130tan140tan150=-30

0 Helpful 0 Interesting 0 Brilliant 0 Confused

tan(60-theta) tan(theta) tan(60+theta) =tan3theta so if theta=10 then N=30

piyush gupta - 7 years, 3 months ago

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