How do you solve this and write in factored form? Sec^2x-secx+tan^2x

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Answer 1 · 2018-07-21T13:27:21

#color(green)(=> (2 sec x + 1) * ( sec x - 1)#

#color(crimson)(1 + tan^2 x = sec ^2 x, " Identity"#

#sec ^2 x - sec x + tan ^2 x#

#=> sec^2 x - sec x + sec^2 x - 1#

#=> 2 sec^2 x - sec x - 1#

#=> 2 sec^2 x - 2 sec x + sec x - 1#

#=> 2 sec x (sec x - 1) + 1 * (sec x - 1)#

#color(green)(=> (2 sec x + 1) * ( sec x - 1)#

Answer 2 · 2018-07-21T13:27:40

#(\sec x-1)(2\sec x+1)#

#\sec^2x-\secx+\tan^2x#

#=\sec x(\sec x-1)+sec^2x-1#

#=\sec x(\sec x-1)+(secx+1)(\sec x-1)#

#=(\sec x-1)(\sec x+\sec x+1)#

#=(\sec x-1)(2\sec x+1)#