tan(θ1+θ2+⋯+θn)=S1−S3+S5+⋯1−S2+S4+⋯
where Si denotes the sum of product of tangent of angles taken i at a time.
For example,tan(θ1+θ2)=S11−S2=tanθ1+tanθ21−tanθ1tanθ2
(This formula is given in my textbook with no derivation or background)
How to derive this?
Answer
Prove that is true for 2 angles, then consider it true for (n−1) angles and prove for n angles.
If you prove it for 2 angles, it will be easy to prove it for n angles (knowing it is true for (n−1) angles) by considering θ1+...+θn−1 is one angle, and θn is the other.
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