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

[Cutie13]

cos 4x + cos 3x/ sin4x - sin 3x
Please somebody check this over!

The answer in the book is: cot (x/2)

 

[cristo]

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).

 

[Cutie13]

cos (4x+3x)
____________
sin (4x+3x)

 

[Cutie13]

or does the x have to be fatored out also?
am i on right track

 

[cristo]

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).