# Trig Identities

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#1
(sec^2x + tan^2x)(cosec^2x + cot^2x) = 1+ 2sec^2xcosec^2x

A bit stuck on what to do here, can anyone help?
Thank you
0
10 months ago
#2
(Original post by mmmmmmm88888)
(sec^2x + tan^2x)(cosec^2x + cot^2x) = 1+ 2sec^2xcosec^2x

A bit stuck on what to do here, can anyone help?
Thank you
Expand brackets, rewrite everything in terms of cos and sin, simplify.

Or if you're feeling brave to do this quicker, when multiplying out brackets keep the sec^2 out as a factor. Then also the product tan with cot will obviously be the term giving the 1. And finally, tan with cosec will give sec term as well. So apart from the 1, all terms have a sec as a factor. Factor it out and simplify the leftover bracket.
Last edited by RDKGames; 10 months ago
0
10 months ago
#3
Notice that sec^2x = 1 + tan^2x and csc^2x =1 + cot^2x
Edit: no you actually don't need this
Last edited by 109Natsu; 10 months ago
0
#4
(Original post by RDKGames)
Expand brackets, rewrite everything in terms of cos and sin, simplify.

Or if you're feeling brave to do this quicker, when multiplying out brackets keep the sec^2 out as a factor. Then also the product tan with cot will obviously be the term giving the 1. And finally, tan with cosec will give sec term as well. So apart from the 1, all terms have a sec as a factor. Factor it out and simplify the leftover bracket.
Thank you! Got it in the end
0
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