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# C2 Trig Identities Watch

1. When solving equations, I sometimes miss out solutions because I've manipulated the equation incorrectly. How can I make sure I don't do this?
For example:

I could divide by tan throughout, but this would miss solutions out.
I know I need to multiply by cos, but how do I know which is the correct thing to do in general for questions like this?
2. (Original post by H0PEL3SS)
When solving equations, I sometimes miss out solutions because I've manipulated the equation incorrectly. How can I make sure I don't do this?
For example:

I could divide by tan throughout, but this would miss solutions out.
I know I need to multiply by cos, but how do I know which is the correct thing to do in general for questions like this?
How would you solve x^2 = x ?
3. (Original post by H0PEL3SS)
When solving equations, I sometimes miss out solutions because I've manipulated the equation incorrectly. How can I make sure I don't do this?
For example:

I could divide by tan throughout, but this would miss solutions out.
I know I need to multiply by cos, but how do I know which is the correct thing to do in general for questions like this?
Just try and make it so that you are manipulating only 1 trig function. Not really sure why you would divide by tan anyway.

Slightly curious, what would you get if you divided through by tan?
4. (Original post by H0PEL3SS)
When solving equations, I sometimes miss out solutions because I've manipulated the equation incorrectly. How can I make sure I don't do this?
For example:

I could divide by tan throughout, but this would miss solutions out.
I know I need to multiply by cos, but how do I know which is the correct thing to do in general for questions like this?
I wouldn't be able to give you advice about a general method for all trig questions. The best possible thing to do in order to avoid these sort of mistakes, in my opinion, would be to practice lots of different questions and hopefully you would be able to try different methods for a particular question quick enough, in your head or maybe on paper, to see which method produces the best results.
5. (Original post by Blobar)
Just try and make it so that you are manipulating only 1 trig function. Not really sure why you would divide by tan anyway.

Slightly curious, what would you get if you divided through by tan?
Wouldn't you end up with 5cos(2θ)=1?
Since tan(x) = sin(x)/cos(x)
6. (Original post by Area_51)
Wouldn't you end up with 5cos(2θ)=1?
Since tan(x) = sin(x)/cos(x)
No, that is the issue, hence why I asked how the OP would solve x^2 = x
7. (Original post by m4ths/maths247)
No, that is the issue, hence why I asked how the OP would solve x^2 = x
I'd solve x^2-x by factorising into x(x-1), but I don't see what you're getting at.
I would have divided by tan to get 5cos(2θ)=1, but I know it misses out solutions.
8. (Original post by H0PEL3SS)
I'd solve x^2-x by factorising into x(x-1), but I don't see what you're getting at.
I would have divided by tan to get 5cos(2θ)=1, but I know it misses out solutions.
The two are closely related. You didin't divide both sides by a function with the algebraic equation I gave yet did divide the trig one by a function (tan2θ)
By writing tan as sin/cos you will keep the two functions and be able to factor them accordingly.

Draw tan(2θ) and 5sin(2θ) on the same axis and see the number points of intersection (as with y = x^2 and y = x)
9. (Original post by m4ths/maths247)
The two are closely related. You didin't divide both sides by a function with the algebraic equation I gave yet did divide the trig one by a function (tan2θ)
By writing tan as sin/cos you will keep the two functions and be able to factor them accordingly.

Draw tan(2θ) and 5sin(2θ) on the same axis and see the number points of intersection (as with y = x^2 and y = x)
I see now. Thanks.

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Updated: April 16, 2014
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