Jacobi series for Bessel's function

Question

Using Jacobi series, prove the following

${J_0}^2+{J_1}^2+{J_2}^2+\cdots=1$

My trial:

$\cos(x\sin θ)=J_0+2J_2\cos(2θ) +2J_4\cos(4θ)+\cdots$

$\sin(x\sinθ)=2\big(J_1\sin(θ) +J_3\sin(3θ)+J_5\sin(5θ)+\cdots\big)$

Squaring both equations and adding them is what I thought we are supposed to do but in this is not enough to solve this equality. How do i proceed from here

Answer 1

Let both of the Jaccobi series then square both of the equations. Now, first take the $\cos^2$ series and apply integration with limits $0$ to $\pi$. which then gives a result of an even number, and then take the second series and repeat