Can you factorise this?

I'm trying to do a question

to solve 4sin x = 3 tan x

so, I converted the tan x

into 4sin x = 3sin x /cos x

so I cross multiplied , for it to be 4sin x 3 Cos x = 3 sin x

I subtratced 3 sin x

Hence = 4sin x 3cos x - 3 sin x = 0

can I factorise, if so, any tips or how would you do it?

Reply 1

Mosa99

15

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Reply 2

FryOfTheMann

7

4sinx = 3 tanx
4sinx = 3sinx/cosx
4sinx -3sinx/cosx = 0
sinx(4-3/cosx) = 0
so either sinx = 0
or 4 = 3/cosx
4cosx = 3
cosx = 3/4

I think this would be a correct way of doing it, I'm not very awake right now though.

P.S: Be wary of just cancelling out sinx when trying to solve, as you will leave out solutions for sinx = 0

(edited 6 years ago)

Original post by KatheO11

I'm trying to do a question

to solve 4sin x = 3 tan x

so, I converted the tan x

into 4sin x = 3sin x /cos x

so I cross multiplied , for it to be 4sin x 3 Cos x = 3 sin x

I subtratced 3 sin x

Hence = 4sin x 3cos x - 3 sin x = 0

can I factorise, if so, any tips or how would you do it?

Your manipulation is off.

4 \sin x = 3\tan x \Leftrightarrow 4 \sin x = \frac{3\sin x}{ \cos x} \Leftrightarrow 4 \sin x \cos x = 3 \sin x

Then move sine over to the LHS and factor it out.

Reply 4

Jpnock

3

Original post by Mosa99

Dividing through by sin(x), in this case, removes some solutions. Instead, everything should be moved to one side, hence making the left-hand side equal to zero. After this the sin(x) should be factorised out and the equation can be solved normally from this point.