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Help..please?? Trigonometric identities....

1. cosec^2x(tan^2x - sin^2x) = tan^2x



and


2. sec x / tanx + cot x = sin x
(edited 13 years ago)
Write them all in terms of sin and cos.

For 1 (specifically), use sec^2 x minus tan ^2 x = 1 after expanding the brackets.

Also, 2 is wrong.
(edited 13 years ago)
Original post by electriic_ink

use sec^2 x + tan ^2 x = 1


Since when?
Reply 3
Avatar for Devillife
Devillife
OP
Original post by electriic_ink
Write them all in terms of sin and cos.

For 1 (specifically), use sec^2 x + tan ^2 x = 1 after expanding the brackets.

Also, 2 is wrong.


huhhhhhhhhhhhhhhhhhhhhhhhhhhhhh?

soooo

1/sin^2x (sin^2x/cos^2x - sin^2x)???????????
Original post by ghostwalker
Since when?


I meant minus :h:
Reply 5
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Slowbro93
20
Have you written 2 wrong?
Reply 6
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Devillife
OP
Original post by cpdavis
Have you written 2 wrong?


oops....yh it should be tan x + cot x...
Reply 7
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Devillife
OP
Original post by ghostwalker
Since when?


really stukkk......:|
Original post by Devillife
huhhhhhhhhhhhhhhhhhhhhhhhhhhhhh?

soooo

1/sin^2x (sin^2x/cos^2x - sin^2x)???????????


Yeah. If you write it in terms of sin/cos it makes it easier to see when you expand it you get 1/cos^2x - 1 = .....
Original post by Devillife
huhhhhhhhhhhhhhhhhhhhhhhhhhhhhh?

soooo

1/sin^2x (sin^2x/cos^2x - sin^2x)???????????


So, cancel what you can, and see how you can apply electriic_ink's corrected ( :p: ) identity.
Original post by Devillife
oops....yh it should be tan x + cot x...


Yh that works, change all the cots and tans into sins and cos, and make the sec x in terms of cos. Then make into one fraction and you should see some cancelling
Reply 11
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Devillife
OP
Original post by electriic_ink
Yeah. If you write it in terms of sin/cos it makes it easier to see when you expand it you get 1/cos^2x - 1 = .....


ryttt..... so ive gt 1/cos^2x -sin^2x/sin^2x so its just 1/cos^2x -1 ooooo
so thats sec^2x -1 ...ahh i get it
Reply 12
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Devillife
OP
Original post by cpdavis
Yh that works, change all the cots and tans into sins and cos, and make the sec x in terms of cos. Then make into one fraction and you should see some cancelling


sec x = 1/cos x

tan x = sinx/cos x

cot x = cos x/sin x


so at the bottom im left with 1/cos x sinx ??
Original post by Devillife
sec x = 1/cos x

tan x = sinx/cos x

cot x = cos x/sin x


so at the bottom im left with 1/cos x sinx ??


:yep: then where would you go from there?
Reply 14
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Devillife
OP
Original post by cpdavis
:yep: then where would you go from there?


i got fractions on both sides .. so i x by cos x????
i would be left with 1/ ?
arghhhhhhhhhhhhhh :s-smilie::|:|:|
1/cos⁡x1/cos⁡xsin⁡x=1cos⁡x×sin⁡xcos⁡x1\frac{1/\cos x}{1/\cos x \sin x} = \frac{1}{\cos x} \times \frac{\sin x \cos x}{1}
Original post by Devillife
i got fractions on both sides .. so i x by cos x????
i would be left with 1/ ?
arghhhhhhhhhhhhhh :s-smilie::|:|:|


you should be at this stage.

1cosx÷1cosxsinx\frac{1}{cosx} \div \frac{1}{cosxsinx}

How how do you divide fractions (hint, what do you do to the second fraction and two the sign)
Reply 17
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Devillife
OP
yayyyy i got it ..... thankyouuuuuuuuuuuuuuuuuuuuuuu :smile::smile::smile::smile::smile:

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