7
votes
Accepted
Summation inside tan(x)
In fact, rewriting $\tan(a_k)$ under the form :
$$\tan(a_k)=\frac{\tfrac{k}{n}-\tfrac{k-1}{n}}{1+\tfrac{k}{n}\tfrac{k-1}{n}}$$
we recognize in the RHS the formula of
$$\tan(a-b)=\frac{\tan(a)-\tan(b)}{...
- 78.7k
1
vote
Finding an angle $\theta$ such that $ \tan \theta = \cot \left(\frac{\theta}3 + \frac{\pi}{12} \right) $
Remember that the co- prefix in trigonometry is short for complementary: evaluating a co-trig function at an angle is the same as evaluating the trig function at the co-angle. And since the complement ...
- 23.4k
1
vote
Splitting restaurant bill
Suppose the 2 other people wish to pay £$x$, where $x$ is just a number. Then the other person wants to pay £$x+10$.
In total, then, $x + x + (x+10) = 3x+10$ pounds is payed.
So we need $3x+10=115$. ...
- 1,661
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