## Ask Singapore Homework?

Upload a photo of a Singapore homework and someone will email you the solution for free.

## Question

secondary 4 | A Maths

** One Answer Below **

Anyone can contribute an answer, even non-tutors.

**Answer This Question**

Hi, can someone help me with the second part 2tan20 + 4tan40 +8tan80 = 9(cot10 - tan10). Thanks!

= 2 (cot 20° - 2 cot 40°) + 4 (cot 40° - 2 cot 80°) + 8 (cot 80° - 2 cot 160°)

= 2 cot 20° - 4 cot 40° + 4 cot 40° - 8 cot 80° + 8 cot 80° - 16 cot 160°

= 2 cot 20° - 16 cot 160°

= cot 10° - tan 10° - 8 (2 cot (180° - 20°))

(Since tan x = cot x - 2 cot 2x, then 2 cot 2x = cot x - tan x)

= cot 10° - tan 10° - 8 (-2 cot 20°)

(Recall the supplementary identity tan (180° - θ) = -tan θ

So cot (180° - 20°) = 1/tan(180° - θ) = 1/-tanθ = -cot θ)

= cot 10° - tan 10° - 8 (tan 10° - cot 10°)

(Since tan x = cot x - 2 cot 2x, then -2 cot 2x = tan x - cot x)

= cot 10° - tan 10° + 8 (cot 10° - tan 10°)

= 9 (cot 10° - tan 10°)

(Shown)

### See 1 Answer