how do you simplify sin^4 heta+sin^2 heta cos^2 heta

Question

how do you simplify sin^4	heta+sin^2	heta cos^2	heta

anonymous · Answer

let sin/theta = s and cos/theta = c for the sake of these equations$$s^4 + s^2c^2$$factorising s^2 we get$$s^2(s^2+c^2)$$this is the identity$$\cos ^2 + \sin^2 =1$$

anonymous · Answer

Therefore answer is simply$$\sin^2$$

mathslover · Answer

Good work @hea , great to see a new user helping someone. Well done, 

@Sophiel44 so the answer will be : $\sin^2 \theta$ , have you got the method hea suggested?

anonymous · Answer

yes I have thanks!

mathslover · Answer

Also, 
$\color{blue}{\mathsf{Welcome}} \space \color{orange}{\cal{To}} \space \color{red}{\mathsf{OpenStudy!!!}}$

anonymous · Answer

How would you do this one :  $$\sin ^{4}\theta+2\sin ^{2}\theta \cos ^{2}\theta +\cos ^{4}$$

mathslover · Answer

$\sin^4 \theta + 2\sin^2 \theta \cos^2 \theta + \cos^4 \theta $ 
can be written as : $(\sin^2 \theta)^2 + 2\sin^2 \theta \cos^2 \theta + (\cos^2 \theta)^2$ 

right?

anonymous · Answer

yes

mathslover · Answer

Put : $\sin^2 \theta = x$ and $\cos ^2 \theta = y$ 

We get now : 
$x^2 + 2 xy + y^2$

anonymous · Answer

then what?

mathslover · Answer

Can you simplify $x^2 +2xy+ y^2$ , I mean factorize it.

anonymous · Answer

yes, (x+y) (x+y)

mathslover · Answer

or (x+y)^2 ?

anonymous · Answer

oh yes

mathslover · Answer

now put x and y as $\sin^2 \theta$ and $\cos^2 \theta$ respectively. What you get?

anonymous · Answer

=1

anonymous · Answer

I see how this works, thank you very much! :)

mathslover · Answer

That's it, Well done sophie. Really great. 
Best of luck for your journey in OpenStudy ... 

Keep helping and getting help on OpenStudy .

anonymous · Answer

officially a fan

mathslover · Answer

best of luck again and thanks!