Question

simplify (cos4x-cos2x)/(sin4x+sin2x) the answer choices are : cotx, tanx, cotxtanx, or 1

Answer 1

let x be 45 deg

(cos180-cos90)/(sin180+sin90)=-1/(1)=-1

so none of the answers are correct, as ctn(45), tan(45), ctn(45)*tan(45), or 1 are not equal to -1

another angle: let x be 30 deg
(cos120-cos60)/(sin120+sin(60)=(-.5-.5)/(.866+.866)=-.577
lets check given answers:
ctn30=1.73
tan30=.577
ctn30*tan30=1
1
none of these are equal to -.577