Question

if x=asin theta + bcos theta and y = a cos theta - b sin theta prove that x²+y²= a²+b²

Answer 1

hope this answer helps you.

Answer 2

Answer:

Step-by-step explanation:

Given: $x=asin{\theta}+bcos{\theta}$ and $y=acos{\theta}-bsin{\theta}$

Now, $x^{2}+y^{2}=(asin{\theta}+cos{\theta})^{2}+(acos{\theta}-bsin{\theta})^{2}$

$x^{2}+y^{2}=a^{2}sin^{2}{\theta}+b^{2}cos^{2}{\theta}+2absin{\theta}cos{\theta}+a^{2}cos^{2}{\theta}+b^{2}sin^{2}{\theta}-2absin{\theta}cos{\theta}$

$x^{2}+y^{2}$=$a^{2}(sin^{2}{\theta}+cos^{2}{\theta})+b^{2}(sin^{2}{\theta}+cos^{2}{\theta})$

$x^{2}+y^{2}$=$a^{2}(1)+b^{2}(1)$

$x^{2}+y^{2}$=$(a^{2}+b^{2})$