Question

if x=Acos o and y= Bcot o show that A2÷x2-B2÷y2=1

Answer 1

you can see your answer

Answer 2

Answer:

Step-by-step explanation:

Given: $x=Acos{\theta}$ and $y=Bcot{\theta}$,

then LHS=$\frac{A^{2}}{x^{2}}-\frac{B^{2}}{y^{2}}$

=$\frac{A^{2}}{A^{2}cos^{2}{\theta}}-\frac{B^{2}}{B^{2}cot^{2}{\theta}}$

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

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

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

=$1$=RHS

Hnece proved