Question

Prove the following trigonometric identities.

If $\frac{x}{a}\cos \theta +\frac{y}{b}\sin \theta =1\mathrm{and}\frac{x}{a}\sin \theta -\frac{y}{b}\cos \theta =1,\mathrm{prove}\mathrm{that}\frac{x^2}{a^2}+\frac{y^2}{b^2}=2$

Answer 1

Given that,

We have to prove

We know that,

Squaring and then adding the above two equations, we have