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# Trig Watch

1. how do i solve sin(theta)cos(theta)-sin(theta)+cos(theta) = 1?
2. (Original post by alesha98)
how do i solve sin(theta)cos(theta)-sin(theta)+cos(theta) = 1?
If you write and it becomes which factorises neatly as i.e:

So that you get two family of solutions:

or .
3. (Original post by alesha98)
how do i solve sin(theta)cos(theta)-sin(theta)+cos(theta) = 1?
Bring the 1 over to the other side and see if you can put the LHS into two brackets.
Spoiler:
Show
sinϴcosϴ - sinϴ + cosϴ - 1 = (sinϴ + ?)(cosϴ - ?)
4. Express sin(theta) as a function of cos(theta) then you should be able to obtain a constant term from the function of cos(theta). This gives you the sin(theta) term but I didn't notice what Zacken had put. Don't listen to me.
5. (Original post by alesha98)
how do i solve sin(theta)cos(theta)-sin(theta)+cos(theta) = 1?
If you're not entirely sure why it factorises the way it does in my post, then consider this:

By pulling out the common factor out .
6. (Original post by Zacken)
If you're not entirely sure why it factorises the way it does in my post, then consider this:

By pulling out the common factor out .
Thankyou so much
7. (Original post by alesha98)
Thankyou so much
You're very welcome!
8. (Original post by Zacken)
If you write and it becomes which factorises neatly as i.e:

So that you get two family of solutions:

or .
so what if i take out as a common factor? do i lose some answers?
9. (Original post by thefatone)
so what if i take out as a common factor? do i lose some answers?
If you divide an equation by something which could be zero then you will lose solutions, for example x^2 - 2x = 0; dividing by x gives x - 2 = 0 -> x = 2, which misses the solution x = 0.
10. (Original post by thefatone)
so what if i take out as a common factor? do i lose some answers?
Well, depends on what you mean. But I don't see how it would be useful.
11. (Original post by Zacken)
Well, depends on what you mean. But I don't see how it would be useful.
i did this

which gave me

then i would solve from there but that doesn't seem right...
12. (Original post by thefatone)
i did this

which gave me

then i would solve from there but that doesn't seem right...
It is right, it's just massively useless. How would you proceed from here?
13. (Original post by Zacken)
It is right, it's just massively useless. How would you proceed from here?
lol i know TeeEm would kill me for this

but i'd continue to solve for values of theta

so

and
14. (Original post by thefatone)
...
That's not how it works. You can only do equate each factor to zero if your equation is of the form .

Otherwise, do you think we can do this: so and ? Is this valid.

Nopes, it is not the case that then or . This is only true if c=0.
15. (Original post by Zacken)
That's not how it works. You can only do equate each factor to zero if your equation is of the form .

Otherwise, do you think we can do this: so and ? Is this valid.

Nopes, it is not the case that then or . This is only true if c=0.
there we go that's what i was looking for
thanks
16. (Original post by thefatone)
there we go that's what i was looking for
thanks
You're welcome.

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