A geometry problem by Rudraksh Sisodia

Geometry Level 3

sin ( 3 a ) = 4 sin ( a ) sin ( x + a ) sin ( x a ) \sin (3a)=4\sin (a) \sin (x+a)\sin (x-a)

Find the smallest positive angle x x (in degrees) such that the above is an identity for all values of a a .


The answer is 60.

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2 solutions

Ahmad Saad
Mar 22, 2016

Aakash Khandelwal
Mar 27, 2016

This and the other one similar for cosine are my favourite trigonometry identities.

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