3 Unit Maths Question (Trigonometry) (1 Viewer)

DSar · Mar 30, 2011

Prove the following identity:

Step-by-step please

Thanks

elbatiolpxeho · Mar 30, 2011

DSar said:

There is no such identity, the thingymabob isn't true for all values of x.

Also, why doesn't the Year 11 forum allow embedded images? Cunt.

Drongoski · Mar 30, 2011

ohex

U r right. To be an identity it must hold for all values of the argument theta. But if we just choose a convenient theta = pi/3 say, we can easily show LHS not equal to RHS.

laplace10 · Mar 30, 2011

lool noobs I think there is a typo

if you change it to (sinx)^2 (tanx)^2 +2sin(x)cos(x) + (cotx)^2 (cosx)^2

then you get LHS = [ sin(x)tan(x) +cot(x)cos(x)] ^2

you prob get somewhere from that

SpiralFlex · Mar 30, 2011

I think it's just a $\cot \theta$ not $\cot^2 \theta$ in the LHS. Assuming the previous statement is true,

$LHS = \sin^2 \theta \tan \theta + \cos^2 \theta \cot \theta + 2\sin \theta \cos \theta$

$(1-\cos ^2\theta)\frac{\sin \theta}{\cos \theta} + (1-\sin^2 \theta)\frac{\cos \theta}{\sin \theta} +2\sin \theta \cos \theta$

$= \frac{\sin \theta}{\cos \theta} - \sin \theta \cos \theta + \frac{\cos \theta}{\sin \theta} - \sin \theta \cos \theta + 2\sin \theta \cos \theta$

$= \frac{\sin \theta}{\cos \theta} + \frac{\cos \theta}{\sin \theta}$

$= \tan \theta + \cot \theta$

$= RHS$

laplace11 · Mar 30, 2011

LOL the OP was a massive noob, can even write the question correctly

DSar · Mar 30, 2011

SpiralFlex said:
I think it's just a $\cot \theta$ not $\cot^2 \theta$ in the LHS. Assuming the previous statement is true,

$LHS = \sin^2 \theta \tan \theta + \cos^2 \theta \cot \theta + 2\sin \theta \cos \theta$

$(1-\cos ^2\theta)\frac{\sin \theta}{\cos \theta} + (1-\sin^2 \theta)\frac{\cos \theta}{\sin \theta} +2\sin \theta \cos \theta$

$= \frac{\sin \theta}{\cos \theta} - \sin \theta \cos \theta + \frac{\cos \theta}{\sin \theta} - \sin \theta \cos \theta + 2\sin \theta \cos \theta$

$= \frac{\sin \theta}{\cos \theta} + \frac{\cos \theta}{\sin \theta}$

$= \tan \theta + \cot \theta$

$= RHS$

Thanks a ton. Appreciate it. I'm guessing you used the 2 Unit Fitzpatrick book?

laplace11 said:
LOL the OP was a massive noob, can even write the question correctly

"Sue me, Dickhead."- Arnold Swarchenegger

SpiralFlex · Mar 30, 2011

DSar said:
Thanks a ton. Appreciate it. I'm guessing you used the 2 Unit Fitzpatrick book?

No. I use 3 unit Cambridge, Fitzpatrick and in the process of Terry Lee Fundamentals.

greenboxes · Mar 31, 2011

Wait, how did you get from the second line to the third line? My trig test is tomorrow, FML >_<

SpiralFlex · Mar 31, 2011

greenboxes said:
Wait, how did you get from the second line to the third line?

Not to fear. I assume you mean,

$(1-\cos ^2\theta)\frac{\sin \theta}{\cos \theta} + (1-\sin^2 \theta)\frac{\cos \theta}{\sin \theta} +2\sin \theta \cos \theta$

TO

$= \frac{\sin \theta}{\cos \theta} - \sin \theta \cos \theta + \frac{\cos \theta}{\sin \theta} - \sin \theta \cos \theta + 2\sin \theta \cos \theta$

All I did was expand the brackets.

RANK 1 · Mar 31, 2011

wtf dude as if u didnt get that, u really need to study more

greenboxes · Mar 31, 2011

I really do, cause I still don't get it...

SpiralFlex · Mar 31, 2011

All part of the learning process.

RANK 1 · Mar 31, 2011

go to mathsonline.com and look at their videos most of them are really simple examples but they still help

RANK 1 · Mar 31, 2011

shame they dont have ext 2

greenboxes · Mar 31, 2011

I feel really dumb but the sharpie I'm working this out with is starting to smell funny, so... could you please explain how you changed 1-cos squared theta into negative sin theta cos theta...?

RANK 1 · Mar 31, 2011

because he expanded it and multiplied 1 with sin theta/cos theta then multiplied cos^2 theta with sin theta/cos theta and the cos theta canceled out giving sin theta cos theta

SpiralFlex · Mar 31, 2011

greenboxes said:
I feel really dumb but the sharpie I'm working this out with is starting to smell funny, so... could you please explain how you changed 1-cos squared theta into negative sin theta cos theta...?

You are not "dumb". We are not expected to get things straight away.

$(1- \cos^2 \theta) \frac{\sin \theta}{\cos \theta}$

Remember we times 1 and $\frac{\sin \theta}{\cos \theta} and -\cos^2 \theta$ times $\frac{\sin \theta}{\cos \theta}$

$= \frac{\sin \theta}{\cos \theta} - \frac{\sin \theta \cos^2 \theta}{\cos \theta}$

= $\frac{\sin \theta}{\cos \theta} - \sin \theta \cos \theta$

RANK 1 · Mar 31, 2011

how do you write the mathematics, do i need a program or is it built into windows

greenboxes · Mar 31, 2011

Oh wait I get it thanks!

3 Unit Maths Question (Trigonometry) (1 Viewer)

Member

Member

Well-Known Member

Banned

Well-Known Member

Banned

Member

Well-Known Member

Member

Well-Known Member

Active Member

Member

Well-Known Member

Active Member

Active Member

Member

Active Member

Well-Known Member

Active Member

Member

Users Who Are Viewing This Thread (Users: 0, Guests: 1)