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# C3 trig identities watch

1. Hi there I have 3 questions which Im unsure about:

1.) tany = √2 siny

1/cot y = 1/√2 cosec y

cot y = √2 cosec y

cot sq y = 2 cosec sq y

cosec sq y-1= 2 cosec sq y

cosec sq y = -1

2.) sinx = √3/8 and 90<x<180, find the exact value of cot x

So i dreq a triangle, with 8 as the hypotenuse, √3 as one of the sides, and found the 3rd side which is √61. Since tan x = √3/√61, cot x
= 1/tanx = 4.5 Is that right?

3.) Show that tan sq x - sin sq x = tan sq x sin sq x

I have no clue how to do this one.

Thanks very much for your time.
2. Where'd you get these questions from?
3. (Original post by calamityx)
Hi there I have 3 questions which Im unsure about:

1.) tany = √2 siny

1/cot y = 1/√2 cosec y

cot y = √2 cosec y

cot sq y = 2 cosec sq y

cosec sq y-1= 2 cosec sq y

cosec sq y = -1

2.) sinx = √3/8 and 90<x<180, find the exact value of cot x

So i dreq a triangle, with 8 as the hypotenuse, √3 as one of the sides, and found the 3rd side which is √61. Since tan x = √3/√61, cot x
= 1/tanx = 4.5 Is that right?

3.) Show that tan sq x - sin sq x = tan sq x sin sq x

I have no clue how to do this one.

Thanks very much for your time.
I'm not sure what you want done about the first one, is it an identity you're meant to prove, if so, you manipulate one side until you have proved that it's the other side.

The second one is right but it says exact value therefore you leave it as rt61/rt3

For the last one, think of difference of two squares
4. (Original post by Clarity Incognito)
The second one is right but it says exact value therefore you leave it as rt61/rt3
No, it should be negative. the range is 90 < X < 180
5. (Original post by Clarity Incognito)
I'm not sure what you want done about the first one, is it an identity you're meant to prove, if so, you manipulate one side until you have proved that it's the other side.
No your not, there not equal...

tan y = √2 sin y

sin y / cos y = √2 sin y

1 = √2 cos y

cos y = 1 / √2

y = 45
6. (Original post by DLS)
No your not, there not equal...

tan y = √2 sin y

sin y / cos y = √2 sin y

1 = √2 cos y

cos y = 1 / √2

y = 45
Hahahaaaaaaaaaaaa, totally corrected, I thought it wasn't but you never know what they can make equal to each other these days. Oh yeah, I better not help people at these suspect times of the morning. *yawns*
7. Thanks so much DLS!

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