Proving Identities

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May 23rd 2010, 05:38 AM
geleen09

Proving Identities

how can you prove this ..

1. sin² [theta] + cos² [theta]/cos² [theta] = |1/cos [theta]|²
2. 1-cos²[theta]/sin [theta] = sin [theta]_
3. 1+cot²[theta]/csc ²[theta]=1
4. csc² [theta]-1/csc²[theta]=cos²[theta]
5. cot [theta] – 1 =csc [theta] – sec [theta]/ sec [theta]
6. cos [theta] / sec [theta] + tan [theta] = 1-sin [theta]
7. csc²[theta] = _cos ² [theta] + cot² [theta] + sin² [theta]
8. 2 cos² [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 ² [theta]=cos² [theta] -2

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

Quote:

Originally Posted by geleen09

how can you prove this ..

1. sin² [theta] + cos² [theta]/cos² [theta] = |1/cos [theta]|²
2. 1-cos²[theta]/sin [theta] = sin [theta]_
3. 1+cot²[theta]/csc ²[theta]=1
4. csc² [theta]-1/csc²[theta]=cos²[theta]
5. cot [theta] – 1 =csc [theta] – sec [theta]/ sec [theta]
6. cos [theta] / sec [theta] + tan [theta] = 1-sin [theta]
7. csc²[theta] = _cos ² [theta] + cot² [theta] + sin² [theta]
8. 2 cos² [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 ² [theta]=cos² [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 $(\sin(\theta))^2+(\cos(\theta))^2=1$

CB
May 23rd 2010, 06:18 AM
TheCoffeeMachine

For #2 as well, you just need to realise that $\cos^2{\theta} = 1-\sin^2{\theta}$ .
For #3: $1+\cot^2{\theta} = \csc^2{\theta}$ . 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??