Asked by Taylor
Hello.
I am trying to simplify the problem, (tan^2x-sec^2x)/cosx, but I am unsure how. Does anyone have any formulas or starting moves for me to begin to simplify this problem, using basic identities?
I am trying to simplify the problem, (tan^2x-sec^2x)/cosx, but I am unsure how. Does anyone have any formulas or starting moves for me to begin to simplify this problem, using basic identities?
Answers
Answered by
Tammy
takes 3 steps:
(tan^2x-sec^2x)/cosx
= (sec^2 x - 1 - sec^2 x)/cos x
= -1/cosx
= -secx
or, if you are not familiar with the identity used, often just changing
everything to sines and cosines will work:
(tan^2x-sec^2x)/cosx
( sin^2 x/cos^2 x - 1/cos^2 x) / cosx
= ( (sin^2 x - 1)/cos^2 x )/cosx
= - cos^2 x / cos^3 x
= -1/cosx
= -secx
(tan^2x-sec^2x)/cosx
= (sec^2 x - 1 - sec^2 x)/cos x
= -1/cosx
= -secx
or, if you are not familiar with the identity used, often just changing
everything to sines and cosines will work:
(tan^2x-sec^2x)/cosx
( sin^2 x/cos^2 x - 1/cos^2 x) / cosx
= ( (sin^2 x - 1)/cos^2 x )/cosx
= - cos^2 x / cos^3 x
= -1/cosx
= -secx
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