Prove that tan x = cot x - 2 cot 2x and hence show that
2 tan 20 + 4 tan 40 + 8 tan 80 = 9(cot 10 - tan 10)
* all units are in degree form.
By substituting using the formula above, I got 2 cot 20 - 16 cot 160. However, I am not able to get 9(cot 10 - tan 10), although they add up to the same value.
May I know how to further carry on from this? Thank you very much!
Note that tan 160 = -tan 20 since tan (180 - x) = -tan x
so 16 cot 160 = -16 cot 20
2 cot 20 - 16 cot 160
2 cot 20 + 16 cot 20
18 cot 20
9 (2 cot 20)
but, from equation, 2 cot 2x = cot x - tan x
Hence, 9 (2 cot 20) = 9 (cot 10 - tan 10)
Regards,
Eagle
(Strategic Tuition)
(ExamWorld)
P.S. May I know whether this is O levels or A levels? I want to add it to ExamWorld
Thanks.
Originally posted by eagle:Note that tan 160 = -tan 20 since tan (180 - x) = -tan x
so 16 cot 160 = -16 cot 202 cot 20 - 16 cot 160
2 cot 20 + 16 cot 20
18 cot 20
9 (2 cot 20)but, from equation, 2 cot 2x = cot x - tan x
Hence, 9 (2 cot 20) = 9 (cot 10 - tan 10)
Regards,
Eagle
(Strategic Tuition)
(ExamWorld)P.S. May I know whether this is O levels or A levels? I want to add it to ExamWorld
Thanks.
Ok, thanks.
It's O levels by the way. (: