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# C3 trigonometric proof help please Watch

1. Hi all,

Can someone help me with proving the following please? I have got to a certain point, but I am not sure after that.

(sec^2 x)/(sec x +1)(sec x - 1) = cosec^2 x

Thank you!
2. What have you done so far?
3. I'd always approach these problems by expanding anything that looks promising. You can expand out (sec x + 1)(sec x - 1) to give you a more familiar trigonometric identity.

Just remember that you can rearrange tan^2 x + 1 = sec^2 x and you'll be fine.
4. (Original post by londoncricket)
Hi all,

Can someone help me with proving the following please? I have got to a certain point, but I am not sure after that.

(sec^2 x)/(sec x +1)(sec x - 1) = cosec^2 x

Thank you!
What have you done so far?
5. (Original post by londoncricket)
Hi all,

Can someone help me with proving the following please? I have got to a certain point, but I am not sure after that.

(sec^2 x)/(sec x +1)(sec x - 1) = cosec^2 x

Thank you!
Hope this helps
(1)expand denominator to give sec2x/sec2x-1
(2)Recall that sin2x+cos2x=1, divide through by cos2x.
(3)Which gives tan2x+1=sec2x => tan2x=sec2x-1
(4)Replace denominator in (1) with tan2x
(5) This gives sec2x/tan2x => (1/cos2x) / (sin2x/cos2x)
(6) This gives cos2x/cos2xsin2x
(7) cancel cos2x terms to give 1/sin2x
(8) 1/sin2x = cosec2x which equals RHS

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