Question

Simplify: 1 - (cos^2t/(1+sint))

Answer 1

\[1-\frac{cos^2(t)}{1+sin(t)} = \frac{1+sin(t)}{1+sin(t)}-\frac{cos^2(t)}{1+sin(t)} = \frac{1+sin(t)+cos^2(t)}{1+sin(t)} \]

Answer 2

And \[cos^2(t)=1-sin^2(t)\]
So: \[\frac{1+sin(t)+cos^2(t)}{1+sin(t)} = \frac{1+sin(t)+1-sin^2(t)}{1+sin(t)} = \frac{-sin^2(t)+sin(t)+2}{1+sin(t)} = -sin(t)+2 \]