Futher Trigo Identities

anpanman SG

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!

eagle SG

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.

bonkysleuth SG