How do you factor sec^2(x)-sec(x)+sin^2(x)*sec^2(x)?

1 Answer
Teddy
Jun 14, 2018

#sec^2x-secx+sin^2xsec^2x=-sec^2x(cosx+2)(cosx-1)#

Explanation:

Start by factoring out #-sec^2x# to get
#-sec^2x(-1+1/secx-sin^2x)#
Using the fact that #secx=1/cosx# and #sin^2x=1-cos^2x#, we get
#-sec^2x(-1+cosx-1+cos^2x)#
Rearranging gives
#-sec^2x(cos^2x-cosx-2)#
Recognizing that this is a quadratic expression of #cosx#, we can factor to get
#-sec^2x(cosx+2)(cosx-1)#

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