Trig Question - unsure on the rules

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beachpanda
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Is anyone able to help? I read recently (on here somewhere) that you shouldn't divide through by a trig function if it could equal zero, as you risk losing solutions. Is that correct?

The mark scheme for this question says one method of solving is to divide through by cos(3θ) and use the tangent identity.

Solve, for 0 < θ < pi, the equation:
sin(3θ) - sqrt(3)cos(3θ) = 0

If that's ok to do then I'm unsure what the rule is?
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HakunaMyTatas
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(i'm gonna call theta t cos i don't know how to get the symbol)

you're right, you shouldn't divide by 0. That is the exact rule. That means you just need to check that cos 3t isn't 0, so a bit of proof by contradiction should sort you out

Pretend that cos 3t = 0.

If you whack cos 3t = 0 in, you get sin 3t - sqrt3 * 0 = 0

sin 3t = 0 = cos 3t.

There is no point on the trig graph where sin x = 0 = cos x, so you know that cos 3t isn't 0, so you can divide by it.
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davros
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(Original post by beachpanda)
Is anyone able to help? I read recently (on here somewhere) that you shouldn't divide through by a trig function if it could equal zero, as you risk losing solutions. Is that correct?

The mark scheme for this question says one method of solving is to divide through by cos(3θ) and use the tangent identity.

Solve, for 0 < θ < pi, the equation:
sin(3θ) - sqrt(3)cos(3θ) = 0

If that's ok to do then I'm unsure what the rule is?
The previous poster is correct.

The general rule is that you shouldn't divide by a quantity if there is a possibility that that quantity could equal zero.

However, we often see a number of trig questions posted that look something like:

Solve sin A + k cos A = 0 for some constant k and some range of angles A.

Now, we know that sin^2A + cos^2A = 1 for all angles A, so there cannot be any value A for which sin A and cos A are both 0. However, the given equation implies that if one of sinA or cosA is 0 then the other one has to be 0 too. Since we know this isn't possible, it is safe to divide by either one to turn it into an equation of the form tan A = r or cot A = s.
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