Math question

**hacker804** · July 30th 2012, 05:38 PM

Hi.Can any one help me with these questions.They are really simple but i cannot seem to get them.Thanks
Q1.Show That:

Q2.Prove that:

Q3.Prove that:

Thanks a lot.

**srirahulan** · July 30th 2012, 06:51 PM

Hi,
I think $Tan(270-\theta)=Cot\theta$
L.H.S
= $tan(270°-x)$
= $\frac{sin(270-\theta}{cos(270-\theta)}$
= $\frac{sin270cos\theta-cos270sin\theta}{cos270cos\theat+sin270sin\theta}$
= $\frac{-cos\theta-0}{0-sin\theta}$
= $\frac{cos\theta}{sin\theta}$
= $cot\theta$

In your Q2
$cos(\alpha+\beta)cos(\alpha-\beta)=cos^2\alpha-sin^2\beta=cos^2\beta-sin^2\alpha$

Take L.H.S

= $\frac{cos(\alpha+\beta)cos(\alpha-\beta)}{1}$
multiply by 2

= $\frac{2cos(\alpha+\beta)cos(\alpha-\beta)}{2}$
= $\frac{cos2\alpha+cos2\beta}{2}$
= $\frac{2cos^2\alpha+2Cos^2\beta-2}{2}$
= $cos^2\alpha+cos^2\beta-1$
= $cos^2\alpha-(1-cos^2\beta)$
= $cos^2\alpha-sin^2\beta$
Or
= $cos^2\beta-(1-cos^2\alpha)$
= $cos^2\beta-sin^2\alpha$

In Your Q3

I think you have a mistake,I think the answer will be $-cos\theta$

**hacker804** · July 30th 2012, 07:24 PM

Thanks a lot for the help.

BTW,can you tell me of a good equation writing software?

Thanks again.

**Prove It** · July 30th 2012, 07:49 PM

Originally Posted by hacker804

Hi.Can any one help me with these questions.They are really simple but i cannot seem to get them.Thanks
Q1.Show That:

Q2.Prove that:

Q3.Prove that:

Thanks a lot.

It's easier in Q.1 to do

$\displaystyle \begin{align*} \tan{\left(270^{\circ} - \theta\right)} &= \tan{\left(180^{\circ} + 90^{\circ} - \theta\right)} \\ &= \tan{\left(90^{\circ} - \theta\right)} \\ &= \frac{\sin{\left(90^{\circ} - \theta\right)}}{\cos{\left(90^{\circ} - \theta\right)}} \\ &= \frac{\cos{\theta}}{\sin{\theta}} \\ &= \cot{\theta} \end{align*}$

**srirahulan** · July 30th 2012, 10:10 PM

Good Idea.Nice work.

**hacker804** · July 30th 2012, 10:45 PM

Thanks for all the help

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