anonymous
  • anonymous
Simplify the trigonometric expression
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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DecentNabeel
  • DecentNabeel
@EllenJaz17 what is the expression
anonymous
  • anonymous
\[\frac{ \sin ^{2} }{ 1-}\]
anonymous
  • anonymous
its supposed to be sin^2theta/1-cos theta

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DecentNabeel
  • DecentNabeel
the answer is 1
DecentNabeel
  • DecentNabeel
correct @EllenJaz17
anonymous
  • anonymous
\[\frac{ \sin ^{2}\theta }{1-cos }\]
anonymous
  • anonymous
and theta is after the cos.
anonymous
  • anonymous
1 Attachment
anonymous
  • anonymous
1 Attachment
anonymous
  • anonymous
1 Attachment
DecentNabeel
  • DecentNabeel
\[\mathrm{Use\:the\:following\:identity}:\quad \:1=\cos ^2\left(x\right)+\sin ^2\left(x\right)\] \[=\frac{\sin ^2\left(θ\right)}{\cos ^2\left(θ\right)-\cos ^2\left(θ\right)+\sin ^2\left(θ\right)}\] \[\frac{\sin ^2\left(θ\right)}{-\cos ^2\left(θ\right)+\cos ^2\left(θ\right)+\sin ^2\left(θ\right)}\] \[\mathrm{Add\:similar\:elements:}\:-\cos ^2\left(θ\right)+\cos ^2\left(θ\right)=0\] \[=\frac{\sin ^2\left(θ\right)}{\sin ^2\left(θ\right)+0}\] \[=\frac{\sin ^2\left(θ\right)}{\sin ^2\left(θ\right)}\] =1
DecentNabeel
  • DecentNabeel
this is the 1 problem
anonymous
  • anonymous
1 Attachment
anonymous
  • anonymous
Those are my answer options
DecentNabeel
  • DecentNabeel
ohhhhhh you needed just answer @EllenJaz17
anonymous
  • anonymous
yeah. Those are my options A-D in the attachments
anonymous
  • anonymous
Would the answer be C?
anonymous
  • anonymous
@DecentNabeel
misty1212
  • misty1212
HI!!
anonymous
  • anonymous
hey
misty1212
  • misty1212
is it just \[\huge \frac{1-\sin(x)}{\cos(x)}\]
anonymous
  • anonymous
So it's b?
misty1212
  • misty1212
no i am still trying to figure out what the original question one
misty1212
  • misty1212
was
anonymous
  • anonymous
Simplify it
1 Attachment
misty1212
  • misty1212
can you repost the original one
DecentNabeel
  • DecentNabeel
\[\mathrm{Simplify}\:\frac{1-\sin \left(θ\right)}{\cos \left(θ\right)}:\quad \left(1-\sin \left(θ\right)\right)\sec \left(θ\right)\]
misty1212
  • misty1212
\[\huge \frac{\sin^2(\theta)}{1-\cos(\theta)}\]
misty1212
  • misty1212
we can do a couple things if that is the original question
anonymous
  • anonymous
Simplify the trigonometric expression (is the question)
misty1212
  • misty1212
perhaps the easiest it to rewrite \(\sin^2(\theta)\) as \(1-\cos^2(\theta)\) then factor
anonymous
  • anonymous
Use the identity sin^2 = 1-cos^2. Then factor it into (1+cos)(1-cos). Then cancel
misty1212
  • misty1212
\[\frac{\sin^2(\theta)}{1-\cos(\theta)}=\frac{1-\cos^2(\theta)}{1-\cos(\theta)}=\frac{(1+\cos(\theta))(1-\cos(\theta))}{1-\cos(\theta)}=1+\cos(\theta)\]
anonymous
  • anonymous
Is that the final answer?
misty1212
  • misty1212
not sure if that is an answer choice, but if it is, pick that one
anonymous
  • anonymous
It is! Thank you!
misty1212
  • misty1212
\[\color\magenta\heartsuit\]

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