Inverse trig from an exam paper

**bbrain** · April 28th 2012, 01:57 PM

See the image for details. I solved the first two parts and got stuck on the last part.

**skeeter** · April 28th 2012, 02:53 PM

Originally Posted by bbrain

See the image for details. I solved the first two parts and got stuck on the last part.

Please note that long-standing MHF policy prohibits assistance on exam questions.

**Prove It** · April 28th 2012, 08:09 PM

Originally Posted by skeeter

Please note that long-standing MHF policy prohibits assistance on exam questions.

Unless it's a past exam or a practice exam. Is it?

**bbrain** · April 29th 2012, 03:38 AM

Originally Posted by Prove It

Unless it's a past exam or a practice exam. Is it?

Yes, it is. CIE Pre U june 2010

**Prove It** · April 29th 2012, 04:23 AM

Well for the first, you'll need to make use of the following identities:

$\displaystyle \begin{align*} \tan{x} &\equiv \frac{\sin{x}}{\cos{x}} \\ \\ \sin{2x} &\equiv 2\sin{x}\cos{x} \\ \\ \cos{2x} &\equiv \cos^2{x} - \sin^2{x} \\ \\ \sin^2{x} + \cos^2{x} &\equiv 1 \\ \\ \tan{\left(\alpha + \beta\right)} &\equiv \frac{\tan{\alpha} + \tan{\beta}}{1 - \tan{\alpha}\tan{\beta}}\end{align*}$

Start by writing $\displaystyle \begin{align*} \tan{3\theta} = \tan{\left(2\theta + \theta\right)}\end{align*}$ . What do you think you would do from here?

**bbrain** · April 29th 2012, 04:49 AM

Originally Posted by Prove It

Well for the first, you'll need to make use of the following identities:

$\displaystyle \begin{align*} \tan{x} &\equiv \frac{\sin{x}}{\cos{x}} \\ \\ \sin{2x} &\equiv 2\sin{x}\cos{x} \\ \\ \cos{2x} &\equiv \cos^2{x} - \sin^2{x} \\ \\ \sin^2{x} + \cos^2{x} &\equiv 1 \\ \\ \tan{\left(\alpha + \beta\right)} &\equiv \frac{\tan{\alpha} + \tan{\beta}}{1 - \tan{\alpha}\tan{\beta}}\end{align*}$

Start by writing $\displaystyle \begin{align*} \tan{3\theta} = \tan{\left(2\theta + \theta\right)}\end{align*}$ . What do you think you would do from here?

I have already done the first part. It's the last part I am stuck on.

**Prove It** · April 29th 2012, 05:08 AM

Originally Posted by bbrain

I have already done the first part. It's the last part I am stuck on.

Why didn't I know that? I guess my psychic powers must be a little off today...

**bbrain** · April 29th 2012, 08:01 AM

Originally Posted by Prove It

Why didn't I know that? I guess my psychic powers must be a little off today...

Anyway could you please help me with the last part?

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