Question

Stuck on a trig proof help!!
If x/a(cosθ)+y/b(sinθ)=1 and x/a(sinθ)-y/b(cosθ)=1 then prove that xsquared/asquared+ysquared/bsquared=2

Answer 1

\[\left({x\over a\cos\theta}+{y\over b\sin\theta}\right)\left({x\over a\cos\theta}-{y\over b\sin\theta}\right)=1\cdot1
\]
simply expand it

Answer 2

That is not what the question says: it's \(x/a\cos \theta\) and later: \(x/a\sin \theta\)

:(

Answer 3

of right... I got lazy and copied my TEX code, forgot to change the things!!

Answer 4

cheat..
we have to proove an ellipse..
use parametric substitution
\[x=\sqrt{2}a\sin t\qquad v=\sqrt{2}b\cos t\]

Answer 5

@Mertsj what thou thinketh?

Answer 6

u,v should now satisfy the other two equations.
\[{\sqrt{2}a\cos\theta\over a\cos\theta}+{\sqrt{2}b\sin\theta\over b\sin\theta}\ne1\]

Answer 7

I can't see it yet.

Answer 8

@jimswig88 are you sure the question is correct?