Rewriting in terms of sine and cosine:

Tanx/secx=sinx/cosx / 1/cosx

=sinx/cosx X cosx/1

=sinx

Approach:

🔻Tanx=sinx/cosx

🔻Secx=1/cosx

🔻To divide multiply by the reciprocal of the denominator

🔻Reduce the resulting product

Factoring:

Cosx-cosxsin^2x=cosx(1-sin^2x)

=cosx X cos^2x

=cos^3x

Approach:

🔹Factor out a common factor of cosx

🔹Use the identity cos^2x=1-sin^2x

🔹Use a property of exponents to multiply cosx and cos^2x

Splitting one into two:

Secx-cosx/secx=

Sex/Secx - Cosx/Secx=

1-cos^2x=

sin^2x

Approach:

🔸a+b/c= a/c + b/c

🔸Secx divided by itself is 1

🔸Secx= 1/cosx therefore cosx/Secx=cos^2x

🔸1-cos^2x=sin^2x