a level mathematics trigonometry help!

solve the equation sec θ = 5 cosec θ for 0 ≤ θ ≤ 2π

I don't know if I'm just confusing myself or this question is hard please help if you can

solve the equation sec θ = 5 cosec θ for 0 ≤ θ ≤ 2π

I don't know if I'm just confusing myself or this question is hard please help if you can

Convert them into sin and cos theta, simplify and divide both sides by cos theta. You should get an equation in tan.

Convert them into sin and cos theta, simplify and divide both sides by cos theta. You should get an equation in tan.

If you're dividing by $\cos \theta$ should you not account for the fact that $\cos \theta = 0$?

If you're dividing by $\cos \theta$ should you not account for the fact that $\cos \theta = 0$?

You're right, that could occur. You should factorise cosx instead.

Isn't it obvious that you should just multiply by sin(theta) and that's it?

Possibly, I haven't looked at the question. Just saw the post about dividing by cos and replied to that. Looking at it, I would multiply by sin theta as well and factorise; but it's okay if other people choose a different way to approach it. :-) (as long as it's valid and doesn't lose you solutions)

If you're dividing by $\cos \theta$ should you not account for the fact that $\cos \theta = 0$?

You're right, that could occur. You should factorise cosx instead.

And factorise? If you multiply by sin(theta) you just get tan(theta)=5.
Don't think it's necessary to multiply everything through and factorise cos(theta) etc.

In this circumstance you can get away with dividing by cosx, since cosx=0 can't be a solution, as sec x would have to be infinite.

Ah, indeed, I didn't read the question properly, I thought it was asec x = bcosec x + c
Yeah, you'd just get tan, you're right!

Yeah I've noticed a lot of people that dive into converting to cosines/sines and multiplying everything through mechanically without thinking a bit to see if there are quicker ways (not talking about you ). Sadly, this kind of thought is very common with most A-Level maths students.

There was a thread that came up with something like this (the way students learn methods instead of understanding) a few days ago, except it was in the context of integration. Can't remember it for the life of me though.

thanks guys i can't believe that i was stuck in this question!! just to check :
1/ i wrote everything down in the form sin and cos
2/ then i multiplied everything by sin theta
3/ as a result i ended up with tan (theta)=5
4/ found the values of tan theta in degrees and got (1.373 and 4.514) correct to 3 decimal places

thanks guys i can't believe that i was stuck in this question!! just to check :
1/ i wrote everything down in the form sin and cos
2/ then i multiplied everything by sin theta
3/ as a result i ended up with tan (theta)=5
4/ found the values of tan theta in degrees and got (1.373 and 4.514) correct to 3 decimal places

Number 4... why have you got it in radians? Does it ask for it in degrees or radians?