Question

Write the expression in terms of sin and cosine and express the result in simplest form.
(Step by step with distribution please.) ( I get lost while distributing "sec θ" to 1 and "cot θ")

sec θ (1 + cot θ) - csc θ (1 + tan θ)

Answer 1

This is where I get lost after distributing \[\frac{ 1 }{ \cos0 } \] to 1

Answer 2

\[\frac{1}{a}(1+a)-\frac{1}{b}(1+\frac{b}{a})\]

Answer 3

you get
\[\frac{1}{a}+1-\frac{1}{b}-\frac{1}{a}\]after distributing

Answer 4

that leaves
\[1-\frac{1}{b}\]

Answer 5

or
\[1-\frac{1}{\sin(x)}\] or even
\[1-\csc(x)\] if you prefer

Answer 6

what are a and b

Answer 7

\[a=\cos(x), b=\sin(x)\] is is 100% algebra, easier to write with \(a,b\) instead of sine and cosine

Answer 8

oh thanks

Answer 9

\[\color\magenta\heartsuit\]