I was browsing through Twitter and came across this very interesting problem by @Pratik Matematik.

There are two ways to solve it, one using geometry, the other relying on trigonometric formulas!

Once again, this is a good moment to pause the article and give the problem a go yourself. When you’re ready, keep reading for the solution. And if you come up with your own approach, feel free to share it in the comments — I’d love to see how you tackled it.

Don’t forget to subscribe to our YouTube channel for more maths puzzles, it’s my goal to reach 100k subscribers someday. 

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Solution 1: Geometry

Notice that the problem really wants us to take a look at the sum of the angles alpha and beta because the angle gamma is simply

To proceed further, we annotate the diagram as follows

We have rotated the blue triangle into the purple region. The two triangles are congruent as we can see.

The whole triangle formed is a right-angled isosceles triangle. Therefore, using the angle sum of triangles, we get

Therefore, the sum is

Well done!

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Solution 2: Trigonometry

Another way to solve it is to use the compound angle formula for tangent.

Notice that

We have

Substituting the values, we get

Therefore

Finally, we have

And that’s our answer. How amazing. Hey, don’t forget to clap👏 the article as a token of appreciation. Thank you 🦁