Further Trigonometry Identity (Proving question)

AI Thread Summary
The discussion focuses on proving the trigonometric identity (sin3A - sinA)/(cosA + cos3A) = tanA. Participants reference key trigonometric identities and attempt to manipulate the expression using sine and cosine addition formulas. There is an emphasis on expanding the terms and simplifying the fractions, although some participants express confusion during the process. Suggestions include using specific identities to facilitate the proof. The conversation highlights the complexity of trigonometric identities and the importance of systematic approaches in solving them.
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1) Question:
Show that (sin3A-sinA)/(cosA+cos3A)=tanA

2) Relevant equations:
tan A=sinA/cos A
1+tan^2A=sec^A
cot A=1/tanA
cot A=cos A/sinA
sin^2A+cos^2A=1
secA=1/cos A
cosecA=1/sinA
1+cosec^2A= cot^2A
sin2A=2sinAcosA
cos2A=1-2sin^2A=cos^2A-sin^2A=2cos^A-1
tan2A=(2tanA)/1-tan^2A

3)Attempt:
(sin3A-sinA)/(cos A+cos3A)
=(2sin3/2Acos3/2A)-(sinAcosA)/(cos^2(1/2)A-sin^2(1/2)A)+(cos^2(3/2)A-sin^2(3/2)A)
I tried expanding but ended up confusing myself...
 
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