# Math Help - trigonometry Addition Formulae (iv)

1. ## trigonometry Addition Formulae (iv)

I have worked out how to do it, just I need to know how to solve it without calculator.

Find the exact value of:
2 cos&#178;15 - 1

this is what i did:

2 cos&#178;15 - 1 so
= cos&#178;15 + sin&#178;15 = 1 side note: sin&#178;15 = 1 - cos&#178;15 hence: 2 cos&#178;15 - 1

then i did:
2 cos&#178;15 - 1 would initially be: cos&#178;15 + sin&#178;15
= cos(15 + 15)
= cos 15 x cos 15 - sin 15 x sin 15
= root 3 / 2

What i wanna know is, i could not of done this without a calculator...
What is the alternative method?
(sorry if i made this very confusing)

2. $\begin{array}{rcl}
2\cos ^2 (A) - 1 & = & \cos (2A) \\
2\cos ^2 (15^o ) - 1 & = & \cos (30^o ) \\
& = & \frac{{\sqrt 3 }}{2} \\
\end{array}$

3. can you give me step by step for:
1 - 2 sin² 22.5
4. $1 - 2\sin ^2 (A) = \cos (2A)$