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Maths P1 doubt on markscheme

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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  ;)

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