solve cosec^2 2x - cot 2x = 1

Hello

The question is to solve

I have tried writing in terms of

and in terms of

without success.

When I caved in and looked at the mark scheme it says to using , which I didn't get. Could someone please give me a clue and or suggest another way.

Thank you

Re: solve cosec^2 2x - cot 2x = 1

Quote:

Originally Posted by

**Furyan** Hello

The question is to solve

I have tried writing

in terms of

and

in terms of

without success.

When I caved in and looked at the mark scheme it says to using

, which I didn't get. Could someone please give me a clue and or suggest another way.

Thank you

Solve each of these equations :)

1 Attachment(s)

Re: solve cosec^2 2x - cot 2x = 1

Re: solve cosec^2 2x - cot 2x = 1

Substitute 1+cot^2(2x) into the equation

Then we'll obtain cot^2(2x)-cot(2x)=0

Factorise the equation

(cot (2x))(cot (2x)-1)=0

cot 2x=0

1/ tan (2x)=0

For 1/tan (2x)=0,

tan (2x)= infinity

So 2x= 90, 270

x= 45, 135

cot (2x)-1=0

1/ tan (2x)=1

tan (2x)=1

2x=45, 225

x=22.5, 112.5

Re: solve cosec^2 2x - cot 2x = 1

Quote:

Originally Posted by

**SkyCapri** Substitute 1+cot^2(2x) into the equation

Then we'll obtain cot^2(2x)-cot(2x)=0

Factorise the equation

(cot (2x))(cot (2x)-1)=0

cot 2x=0

1/ tan (2x)=0

For 1/tan (2x)=0,

tan (2x)= infinity

So 2x= 90, 270

x= 45, 135

cot (2x)-1=0

1/ tan (2x)=1

tan (2x)=1

2x=45, 225

x=22.5, 112.5

Don't forget that the cotangent function is periodic every , so you also need to add all integer multiples of this.

Re: solve cosec^2 2x - cot 2x = 1