7 votes

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)}{...
Jean Marie's user avatar
  • 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 ...
Sammy Black's user avatar
  • 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 $3x+10=115$. ...
Robin's user avatar
  • 1,661

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