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3 years ago

Factor sec^2x-secx+tan^2x

Mathematics

1 answer:

marysya [2.9K]3 years ago

6 0

Answer:

sec²(x) - sec(x) + tan²(x) = (sec(x) - 1)(2sec(x) + 1)

Step-by-step explanation:

sec²(x) - sec(x) + tan²(x) =

= sec²(x) - sec(x) + [sec²(x) - 1]

= sec²(x) - sec(x) + [(sec(x) + 1)(sec(x) - 1)]

= sec(x)[sec(x) - 1] + [(sec(x) + 1)(sec(x) - 1)]

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

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

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