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- Admin
- #1

- Feb 14, 2012

- 3,909

Solve for $y $ if $\tan 4y=\dfrac{\cos y-\sin y}{\cos y +\sin y}$.

- Thread starter anemone
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- Thread starter
- Admin
- #1

- Feb 14, 2012

- 3,909

Solve for $y $ if $\tan 4y=\dfrac{\cos y-\sin y}{\cos y +\sin y}$.

- Nov 4, 2013

- 428

Solve for $y $ if $\tan 4y=\dfrac{\cos y-\sin y}{\cos y +\sin y}$.

We can rewrite the RHS as:

$$\tan 4y=\frac{1-\tan y}{1+\tan y}=\tan\left(\frac{\pi}{4}-y\right)$$

$$\Rightarrow 4y=n\pi+\frac{\pi}{4}-y$$

Only n=0 gives a solution in the specified range, hence

$$y=\frac{\pi}{20}$$

- Admin
- #3

- Mar 5, 2012

- 9,416

How did you get that?$$\frac{1-\tan y}{1+\tan y}=\tan\left(\frac{\pi}{4}-y\right)$$

It's not something you had to learn by heart did you?

- Nov 4, 2013

- 428

Nope.It's not something you had to learn by heart did you?

I used the following formula:

$$\tan(a-b)=\frac{\tan(a)-\tan(b)}{1+\tan(a)\tan(b)}$$

with $a=\pi/4$ and $b=y$.