anonymous
  • anonymous
Use basic identities to simplify the expression. (cos of theta^2 / sin of theta ^2) + csc θ sin θ
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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Nnesha
  • Nnesha
\[\huge\rm \frac{ \cos^2 \theta }{ \sin ^2 \theta } +\csc \theta \sin \theta \] like this ?
Nnesha
  • Nnesha
write csc in terms of sin or cos what's the definition of csc ?? like sec = 1/cos csc = ??
anonymous
  • anonymous
csc = 1/sin theta would I multiply sin theta * 1/sin theta and get 1?

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Nnesha
  • Nnesha
yes that's right :-)
Nnesha
  • Nnesha
and cos /sin = what ? :-) remember tan and cot are reciprocal of each other
anonymous
  • anonymous
(1/ sec theta)^2 /(1 / csc theta)^2?? I'm not really sure how to simplify that :(
Nnesha
  • Nnesha
well that's right but simple way is to change cos/sin to cot \[\tan =\frac{ \sin }{ \cos } ~~\cot=\frac{ \cos }{ \sin }\]
Nnesha
  • Nnesha
so cos^2 theta over sin ^2 theta = cot^2 theta
anonymous
  • anonymous
is there a way to simplify that further?
Nnesha
  • Nnesha
yes
Nnesha
  • Nnesha
\[\huge\rm\color{blue}{ \frac{ \cos^2 \theta }{ \sin ^2 \theta } }+\color{reD}{\csc \theta \sin \theta} \] \[\large\rm \color{blue}{ \cot^2 \theta} +\color{red}{1} = ???\] which is equal to what ??it's an identity
anonymous
  • anonymous
pythagoras? csc^2 theta?
Nnesha
  • Nnesha
yes right cot^2 + 1 = csc^2 x
anonymous
  • anonymous
omg thank you! identities confuse me so much :)
Nnesha
  • Nnesha
my pleasure :-) and practice!! :-)

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