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Core 3 Trig Help!!

I'm not sure how to answer this question;

Solve the following equation for the range 0< x < 360 (inclusive);

cot^2 x + 3 = 3cosec x

I've tried changing the cot^2 into cosec, and the cosec into cot, but I just cannot seem to figure the answer out :frown:

(I'd ask my teacher but she isn't in until our lesson next week then the homework is due, and everyone is stuck!)

Reply 1

xboxaddict

Try writing the cot in terms of cos and sin :smile:

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Reply 2

Hasufel

we first need to hget the equation to a form where we can solve it:

one way of doing this is that we could start by using sin and cos for the cotan and cosec:

\displaystyle \frac{cos^{2}(x)}{sin^{2}(x)}+3= \frac{3}{sin(x)}

then multiply both sides by

sin^{2}(x)

, (stating that sin(x) is not equal to zero)

and re-arrange to get:

cos^{2}(x)+3sin^{2}(x) \equiv (cos^{2}(x)+sin^{2}(x))+2sin^{2}(x) \equiv 1+2sin^{2}(x)=3sin(x)=RHS

re-arrange as a quadratic in sin and solve...

(edited 10 years ago)

Reply 3

the bear

or use the relationship

1 + cot²x = cosec²x

Reply 4

xboxaddict

Original post by the bear

or use the relationship

1 + cot²x = cosec²x

Yeah this is easier, maybe you got the identity wrong when you tried to use it OP?

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Reply 5

iElvendork

I think I was heading in the right direction, I just forgot the third identity (cos^2 + sin^2 = 1) which I could use!
Thanks for your help guys :smile: