Practice problem
Compute the value of the sum 11+tan30∘+11+tan310∘+11+tan320∘+11+tan330∘+11+tan340∘+11+tan350∘+11+tan360∘+11+tan370∘+11+tan380∘.\begin{align*} \frac{1}{1 + \tan^3 0^\circ} &+ \frac{1}{1 + \tan^3 10^\circ} + \frac{1}{1 + \tan^3 20^\circ}\\ &+ \frac{1}{1 + \tan^3 30^\circ} + \frac{1}{1 + \tan^3 40^\circ} \\ &+ \frac{1}{1 + \tan^3 50^\circ} + \frac{1}{1 + \tan^3 60^\circ}\\ &+ \frac{1}{1 + \tan^3 70^\circ} + \frac{1}{1 + \tan^3 80^\circ}. \end{align*}1+tan30∘1+1+tan310∘1+1+tan320∘1+1+tan330∘1+1+tan340∘1+1+tan350∘1+1+tan360∘1+1+tan370∘1+1+tan380∘1.
(Hint: What is 11+x3+11+(1/x)3\frac{1}{1+x^3} + \frac{1}{1+(1/x)^3}1+x31+1+(1/x)31?)
Source: Math Prize for Girls
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Type a concept, like “slope” or “photosynthesis”.
