How do you prove sec x - cos x = sin x tan x?

1 Answer
George C.
Nov 13, 2015

See explanation...

Explanation:

sec(x) = 1/cos(x)

tan(x) = sin(x)/cos(x)

sin^2(x) + cos^2(x) = 1

So:

sec(x) - cos(x)

= 1/(cos(x)) - cos(x)

=1/(cos(x)) - cos^2(x)/cos(x)

=(1-cos^2(x))/cos(x)

=(sin^2(x))/cos(x)

=sin(x)sin(x)/cos(x)

=sin(x)tan(x)

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