(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Simplify and write the trigonometric expression in terms of sine and cosine:

(sec (t) - cos (t))/sec (t) = (f(t))^2

2. Relevant equations

sec (t)=1/cos (t)

3. The attempt at a solution

(sec (t) - cos (t))/sec (t)

= ((1/cos (t))-cos(t)) / (1/cos (t))

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

From here, can I take the entire numerator, ((1-cos^2(t))/cos(t)), and divide it by one? This way I can do division of two rational numbers to get:

= cos(t)*((1-cos^2(t))/cos(t))

=1-cos^2(t) = sin^2(t) = (f(t))^2

so f(t)=sin (t)

I am quite sure this is the right answer, but I am wondering if the method I used is correct math. Thanks for your help everyone.

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# Homework Help: Simplifying trig expression

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