Prove the conjecture fx sin3x sinx cos3x cosxSolutionfx s

Prove the conjecture . f(x) = sin(3x) /sin(x) cos(3x)/ cos(x)

Solution

f(x) = sin(3x) /sin(x) cos(3x)/ cos(x)

use the formula : sina-b) = sinacosb -cosasinb

= [ sin(3x)cosx -cos(3x)sinx]/cosx*sinx

=[ sin(3x-x)/cosx*sinx

= sin2x/cosx*sinx

=2sinxcosx/cosx*sinx

=2