How do u prove tan (x ) = sec (x )-1?

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Answer 1 · 2018-03-05T22:32:10

See below

We start with the Pythagorean identity

#sin^2x+cos^2x =1#

We then divide through by #cos^2x#

#sin^2x/cos^2x+cos^2x/cos^2x=1/cos^2x#

We now simplify using the definitions of reciprocal trig functions

#tan^2x+1=sec^2x#

The final step is trivial to give

#tan^2x=sec^2x-1#, as required. #square#