Question

sin(1+cot^2)

Answer 1

Write everything in terms of sin and cos

\[\large sin(x)(1 + \frac{cos^2(x)}{sin^2(x)})\]

Multiply the \(\large sin(x)\) through
\[\large sin(x) + \frac{cos^2(x)sin(x)}{sin^2(x)}\]
\[\large sin(x) + \frac{cos^2(x)\cancel{sin(x)}}{sin^\cancel{2}(x)}\]
\[\large sin(x) + \frac{cos^2(x)}{sin(x)}\]
Get those over a common denominator (sin) here
\[\large \frac{sin^2(x)}{sin(x)} + \frac{cos^2(x)}{sin(x)}\]
Combine them
\[\large \frac{sin^2(x) + cos^2(x)}{sin(x)} \]

Remember the identity \(\large sin^2(x) + cos^2(x) = 1\)
\[\large \frac{1}{sin(x)}\]
\[\large csc(x)\]