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# Trig help watch

The question is to prove the identity:
(sec^2x + tan^2x)(cosec^2x + cot^2x) = 1+ 2sec^2xcosec^2x

btw sec^2x means sec squared x idk if i wrote that clearly.

Anyway, the hint given on the sheet is to replace both tan squared x and cot squared x with identities and expand the brackets.

I did that and I got
(2sec^2x -1)(2cosec^2x -1)

and when expanded that is
4cosec^2xsec^2x -2sec^2x - 2cosec^2x +1

but I dont know if thats wrong or right, and if it is right how would I equate that to 1 + 2sec^2xcosec^2x

2. (Original post by _s_ox)

The question is to prove the identity:
(sec^2x + tan^2x)(cosec^2x + cot^2x) = 1+ 2sec^2xcosec^2x

btw sec^2x means sec squared x idk if i wrote that clearly.

Anyway, the hint given on the sheet is to replace both tan squared x and cot squared x with identities and expand the brackets.

I did that and I got
(2sec^2x -1)(2cosec^2x -1)

and when expanded that is
4cosec^2xsec^2x -2sec^2x - 2cosec^2x +1

but I dont know if thats wrong or right, and if it is right how would I equate that to 1 + 2sec^2xcosec^2x

It's right; try writing the bit I've bolded in terms of sine and cosine (i.e using secx = 1/cosx, cosecx = 1/sinx), and go from there.

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Updated: October 28, 2015
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