# HELP! Write in terms of sine and cosine then simplify: (secx-cosx)/sinx?

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I cannot figure this out to save my life…the answer in the back of my textbook says it simplifies to tanx but I just can’t figure out how to get to that…

• I’m not 100% sure but this is what i get.

secx-cosx/sinx

=1/cosx – cosx / sinx (because secx = 1/cosx)

= 1-cos^2x/cosx / sinx (when u obtain a common denominator)

=sin^2x/cosxsinx (because 1-cos^2 = sin^x and therefore u can cancel out the square of sin^2x with sinx)

=sinx/cosx

=tanx

hope this helped 🙂

• sec x = 1/cos x

Take the numerator : sec x – cos x = 1/cos x – cos x

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

= sin^2 x/cos x

divide by sin x to get sinx/cosx = tan x

• sec = 1/cos.

So, eqn bcom,

((1/cosx)-cosx)/sinx.

Cross multiply the numerator. So,

(1-cos^2(x))/cosx.sinx

1-cos^2(x)=sin^2(x).

Simplify the rest..

• We know sec x = 1 / cos x. So then we have

([1 / cos x] – cos x) / sin x

= (1 – cos^2 x) / sin x cos x (multiplying numerator & denominator by cos x)

= sin^2 x / sin x cos x

= sin x / cos x

= tan x

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