C4 trigs

2sin2x = cosx
4sinxcosx = cosx
cannot divide by cosx because some values are lost

sinx=cos(x+120)
sinx=cosxcos120-sinxsin120
sinx=-0.5cosx-(sqrt(3)/2)sinx
2sinx=-cosx-sqrt(3)sinx
Here you have to divide by cosx in order for the result to be solved

How am I supposed to know when dividing will cause some roots to be lost or not?

Reply 1

davros

16

Original post by helpme456

2sin2x = cosx
4sinxcosx = cosx
cannot divide by cosx because some values are lost

sinx=cos(x+120)
sinx=cosxcos120-sinxsin120
sinx=-0.5cosx-(sqrt(3)/2)sinx
2sinx=-cosx-sqrt(3)sinx
Here you have to divide by cosx in order for the result to be solved

How am I supposed to know when dividing will cause some roots to be lost or not?

Always try to factorize wherever possible.

Your first problem can be written as (something) X cos x = 0, so either cox x = 0 or something = 0 and you have to check both possibilities.

Your second problem is of the form a sinx = bcos x. If cos x were 0 then sin x would have to be 0 too, but there are no angles for which this is true, so it is safe to divide by cos x.