I have an integral as follows:
$$\int_0^T \cos\theta\cdot dt = xT$$
where $\theta$ is a function of $t$
I also have,
$$\int_0^T \sin\theta\cdot dt = y$$
I want to solve for $T$.
If the integrals were indefinite, I could have differentiated the second one and gotten $\theta$ as a function of $t$ in terms of $y$. Integrating that would have got me $xT$, but unfortunately, I don't see how I can do that as the integrals are under limits.
I also thought of substituting $\cos\theta$ as $\sqrt{1 - \sin^2\theta}$ and then somehow simplifying so that I get it in terms of the left hand side of the second equation but was unsuccessful.
I am certain it is possible since the second integral is a sine of a function that is common to both integrals, there must be enough information contained in the second equation to completely determine the first integral. I just don't know how to extract it.
How do I go about it? I just learnt integration recently, and I'm not all that familiar with the various techniques.