Question

Use basic identities to simplify the expression.

(cos of theta^2 / sin of theta ^2) + csc θ sin θ

Answer 1

\[\huge\rm \frac{ \cos^2 \theta }{ \sin ^2 \theta } +\csc \theta \sin \theta \]
like this ?

Answer 2

write csc in terms of sin or cos
what's the definition of csc ??
like sec = 1/cos
csc = ??

Answer 3

csc = 1/sin theta
would I multiply sin theta * 1/sin theta and get 1?

Answer 4

yes that's right :-)

Answer 5

and cos /sin = what ? :-)
remember tan and cot are reciprocal of each other

Answer 6

(1/ sec theta)^2 /(1 / csc theta)^2??
I'm not really sure how to simplify that :(

Answer 7

well that's right but simple way is to change cos/sin to cot
\[\tan =\frac{ \sin }{ \cos } ~~\cot=\frac{ \cos }{ \sin }\]

Answer 8

so cos^2 theta over sin ^2 theta = cot^2 theta

Answer 9

is there a way to simplify that further?

Answer 10

yes

Answer 11

\[\huge\rm\color{blue}{ \frac{ \cos^2 \theta }{ \sin ^2 \theta } }+\color{reD}{\csc \theta \sin \theta} \]
\[\large\rm \color{blue}{ \cot^2 \theta} +\color{red}{1} = ???\]
which is equal to what ??it's an identity

Answer 12

pythagoras? csc^2 theta?

Answer 13

yes right cot^2 + 1 = csc^2 x

Answer 14

omg thank you! identities confuse me so much :)

Answer 15

my pleasure :-)
and practice!! :-)