Question

Use basic trigonometric identities to simplify the expression:
3sin3 (x) csc(x) + cos2 (x) + 2cos (−x) cos (x) = ?

Answer 1

is it 3sin^3(x) or 3sin(3x)?

Answer 2

oh i forgot the carets its 3sin^3 (x) csc(x) + cos ^2 (x) +2cos (-x) cos (x)

Answer 3

lets start with the first term 3sin^3 (x) csc(x)

Answer 4

csc(x) is the same as 1/sinx

Answer 5

yess so it would be like 3sin^3 (x) 1/sinx

Answer 6

ya, so what would that simplify to?

Answer 7

2sin^3?

Answer 8

no, it should be 3sin^2x

Answer 9

one of the sinx will cancel

Answer 10

ohh okay

Answer 11

\(\bf 3sin^3(x) csc(x) + cos^2 (x) + 2cos (-x) cos (x)\qquad
\begin{cases}
csc(x)=\frac{1}{sin(x)}\\
cos(-x)=cos(x)
\end{cases}
\\ \quad \\
3\cancel{sin^3(x)}\cdot {\color{brown}{ \cfrac{1}{\cancel{sin(x)}} }} + cos^2 (x) + 2cos ({\color{brown}{ x}}) cos (x)
\\ \quad \\
3sin^2(x)+cos^2(x)+2cos(x)cos(x)
\\ \quad \\
\textit{what's }cos(x)cos(x)=?\)