Go Tangent.. :D
Geometry
Level
1
Find the value of
(tan 1)(tan 2)(tan 3) ... (tan 89)
All terms are in degrees.
The answer is 1.
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1 solution
(tan 1)(tan 2)(tan 3) ... (tan 89) ------> (tan 89)(tan 1)(tan 2)(tan 88) ... (tan 45)
we know that:
tan x = 1/(cot x) = 1/(tan 90 - x)
then,
tan 1 = 1/(tan89)
tan 2 = 1/(tan 88)
...
then,
(tan 89)(tan 1)(tan 2)(tan 88) ... (tan 45) -----> (tan 89)(1/(tan89))(tan88)(1/(tan88)) ... (tan45)
------> tan 45
------> 1
Final answer: 1