- #1

Radwa Kamal

- 12

- 0

**HELP! trigonometry**

## Homework Statement

without using calculator:

prove that: sin18 = √5-1/4

## Homework Equations

Double-angle formulae

sin 2a = 2sin a.cos a

cos 2a = cos^2a - sin^2a = 1 - 2sin^2a = 2cos^2a - 1

sin^2 a + cos^2 a=1

## The Attempt at a Solution

let 18=a

sin a = sin(90 - a) = cos 4a

cos 4a = 1 - 2sin^2 2a

= 1 - 2(2sin a.cos a)^2

= 1 - 2(4sin^2 a.cos^2 a)

= 1 - 8sin^2 a.cos^2 a

= 1 - 8sin^2a(1-sin^2a)

= 1 - 8sin^2a + 8sin^4a

i can't go further than that ?!