USA Math Olympiad (USAMO) Question | Prove Trigonometric Identity | Trigonometry

This is a USAMO (USA Math Olympiad) question. How to prove this trigonometric identity? This video will first derive a trigonometric identity and then apply it to complete the proof.

[john]

Challenging question, brilliant solution!

[AajanmaHindu]

Gr8 problem, Gr8 solution! Thank you, Dr. Wang!🙏

[fhffhff]

делая все аналогично, доказывается, что ...=cos1°/sin²1°.

[xlxxgdx]

Let sum=S
Multiply cos1 on both the sides.
Note: cos1=
On expanding we get,
S×cos1= 1+tan0×tan1 + 1+tan1×tan2 +....1+tan88×tan89.
We know that,
Therefore,
tan(x-y)=tan1,
S×cos1×tan1= tan1-tan0
tan2-tan1



tan89-tan88
On cancelation
S×cos1×tan1= tan89-tan0
S×cos1×tan1= cot1
S×sin1=cot1
S=(cos1)/(sin1)^2