# Proving Identities

• May 23rd 2010, 05:38 AM
geleen09
Proving Identities
how can you prove this ..

1. sin˛ [theta] + cos˛ [theta]/cos˛ [theta] = |1/cos [theta]|˛
2. 1-cos˛[theta]/sin [theta] = sin [theta]_
3. 1+cot˛[theta]/csc ˛[theta]=1
4. csc˛ [theta]-1/csc˛[theta]=cos˛[theta]
5. cot [theta] – 1 =csc [theta] – sec [theta]/ sec [theta]
6. cos [theta] / sec [theta] + tan [theta] = 1-sin [theta]
7. csc˛[theta] = _cos ˛ [theta] + cot˛ [theta] + sin˛ [theta]
8. 2 cos˛ [theta]-1 =cos (4th power) [theta] –sin (4th power) [theta]
9. cos [theta]/1+sin [theta] + cos [theta] /1-sin [theta] = 2/ cos theta
10. sin (4th power) [theta]-1/cos ˛ [theta]=cos˛ [theta] -2

(Nod)(Nod)(Nod)
• May 23rd 2010, 05:59 AM
CaptainBlack
Quote:

Originally Posted by geleen09
how can you prove this ..

1. sin˛ [theta] + cos˛ [theta]/cos˛ [theta] = |1/cos [theta]|˛
2. 1-cos˛[theta]/sin [theta] = sin [theta]_
3. 1+cot˛[theta]/csc ˛[theta]=1
4. csc˛ [theta]-1/csc˛[theta]=cos˛[theta]
5. cot [theta] – 1 =csc [theta] – sec [theta]/ sec [theta]
6. cos [theta] / sec [theta] + tan [theta] = 1-sin [theta]
7. csc˛[theta] = _cos ˛ [theta] + cot˛ [theta] + sin˛ [theta]
8. 2 cos˛ [theta]-1 =cos (4th power) [theta] –sin (4th power) [theta]
9. cos [theta]/1+sin [theta] + cos [theta] /1-sin [theta] = 2/ cos theta
10. sin (4th power) [theta]-1/cos ˛ [theta]=cos˛ [theta] -2

(Nod)(Nod)(Nod)

Put brackets in so we are not guessing what you mean.

What have you done, for instance with #1

You should know Pythagoras's theorem $\displaystyle (\sin(\theta))^2+(\cos(\theta))^2=1$

CB
• May 23rd 2010, 06:18 AM
TheCoffeeMachine
For #2 as well, you just need to realise that $\displaystyle \cos^2{\theta} = 1-\sin^2{\theta}$.
For #3: $\displaystyle 1+\cot^2{\theta} = \csc^2{\theta}$. The same idea goes for #3.
Similar ideas for the rest of them. Take care of the brackets, though, or learn the latex.
• May 24th 2010, 05:00 AM
geleen09
can you help to solve those??