Can you Simplify the Trigonometric Expression: cos 4x + cos 3x/ sin4x - sin 3x?

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The discussion revolves around simplifying the trigonometric expression cos 4x + cos 3x / sin 4x - sin 3x. Participants suggest using trigonometric identities, particularly the sum formulas for sine and cosine, to rewrite the expression. There is confusion about whether to factor out x or expand the functions. The correct approach involves expressing cos(4x) in terms of cos(3x + x) to facilitate simplification. The final answer provided in the book is cot(x/2), which participants are trying to verify through these methods.
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cos 4x + cos 3x/ sin4x - sin 3x
Please somebody check this over!

The answer in the book is: cot (x/2)
 
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What do you mean by check this over? You've not done anything yet! Try expanding the trigonometric functions so that they end up in terms of cos(x) and sin(x).
 
cos (4x+3x)
____________
sin (4x+3x)
 
or does the x have to be fatored out also?
am i on right track
 
No. Have you come across formulae, for general a and b, for sin(a+b) and cos(a+b)? If so, try writing cos(4x) as cos(3x+x).
 

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