Verify using trig identitites

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TNVolnteer

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Nov 11, 2009
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My daughter has three problems that she just doesn't understand. Can anyone assist?

1) sin1/2xcosx-sin5/2xcosx = cos3x
2) cos2? – sin2? = 1-sin2?
3) sec4?-tan4? = 1+2tan2?

Thanks in advance!
 
TNVolnteer said:
My daughter has three problems that she just doesn't understand. Can anyone assist?

1) sin1/2xcosx-sin5/2xcosx = cos3x
2) cos2? – sin2? = 1-sin2?
3) sec4?-tan4? = 1+2tan2?

Thanks in advance!
Click to expand...

Yes we can assist.

All these problems require use of "angle summation" and "double angle" formulae.

Please instruct your daughter to show us her work, indicating exactly where she is stuck - so that we know where to begin to help her.
 
She said that she just doesn't know where to begin. If you could just suggest where to start, that would be a big help.
 
To start, apply the formulas mentioned earlier. :wink:
 
Thanks! That helped! She had another one on tonight's homework. Can you help with it, too?

secxsinx = cosxsinx
sec[sup:2dh0l4xg]2[/sup:2dh0l4xg]x+csc[sup:2dh0l4xg]2[/sup:2dh0l4xg]x
 
TNVolnteer said:
Thanks! That helped! She had another one on tonight's homework. Can you help with it, too?

secxsinx = cosxsinx
sec[sup:87mcdli3]2[/sup:87mcdli3]x+csc[sup:87mcdli3]2[/sup:87mcdli3]x
Click to expand...

Start with the left-hand-side(LHS) Convert all the terms to sine and/or cosine.

\(\displaystyle \frac{sec(x)\cdot sin(x)}{sec^2(x) + csc^2(x)} \, = \, \frac{\frac{1}{cos(x)}\cdot sin(x)}{\frac{1}{cos^2(x)} + \frac{1}{sin^2(x)}}\)
 
Ok. And then on the denominator would you find a common denominator to add the fractions?
 
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