Maths P1 doubt on markscheme

[cashem'up]

question from s06 p1 maths......... i have a doubt the ms gives only two values but i get 4.........

sin 2x + 3cos2x = 0 between 0 and 180 solve....

initially i divided by cos2x to get tan2x=3 and found two values 54.2 and 144.2
but then i did

cos2x(tan2x+3)=0 by taking cos 2x in common then i also get values of 45 and 135 but its not there in the MS........have i done any mistake.........help.

[Meticulous]

Divide both sides by cos2x:
Tan2x+3=0
Tan2x=-3
2tanx/1-tan2x=-3
2tanx=-3+3tan2x
3tan2x-2tanx-3=0
Tanx= 1.387, or tanx= -0.720
Therefore, x= 54.2, -35.75
Now use the tan graph or the ASTC rule to find the other angles possible:
X= 54.2, 234.2 -35.75, 144.5

Therefore, x= 54.2, 144.5

[nid404]

sin2x+3cos2x=0

divide by cos2x u get

tan2x+ 3=0

tan2x=-3
2x= tan^-1 (-3)
2x=-71.6
x=-35.5
the range is 0-180

period of a tan curve is pi...in this case pi/2 (since it's tan 2x)

x=-35.5+180 =144.5
x=-35.5+90=54.5

[Meticulous]

You use the periodicity method. Quite helpful I must say.

[nid404]

yup. Faster 

[cashem'up]

yup. Faster 

hey thanks guy nid404 and gladiator......... i did the same as wat nid did ...... by the periodicity method however in the 2nd method i attempted i am getting 4 answers where  took cos2x is taken common... how is it wrong......

[nid404]

can you show how you derived your answer?

I can then help rectify

[Meticulous]

Use periodicity when you're PERFECT at using it. Other wise you'll lose track.

[cashem'up]

can you show how you derived your answer?

I can then help rectify

see i have
sin 2x + 3cos2x = 0
now if i take cos 2x common then
cos2x(sin2x/cos2x +3)
so cos2x(tan2x+3)=0
now one ans is tan2x= -3 and as u did by the periodicity method above get 2 answers
however another would also be cos2x=0 and so u get 2 more answers 45 and 135...................... would that be correct i dont find nethin wrong in it except the fact that its not in the MS

[nid404]

wait...how on earth do you get cos2x=0 ?

[Meticulous]

He factorised the equation. So now either cos2x=0, or tan2x+3=0

[nid404]

aaah.....ok..

Should give you the same answer. I'll try

[cashem'up]

guyzz....ne solution any idea........... 

[Meticulous]

Use my method. Works all the time. Takes time, but it's structured and pretty good.

[nid404]

ohk....now i realize what's wrong in ur case.

you cannot take cos2x common...

they are 2 separate terms.