Proving Identities

May 2010
2
0
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)
 

CaptainBlack

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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 \(\displaystyle (\sin(\theta))^2+(\cos(\theta))^2=1\)

CB
 
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Mar 2010
715
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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.