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Which of the following is true for all possible non-zero choices of integers $m,n;m\neq n$, or all possible non-zero choices of real numbers $p,q;p\neq q$, as applicable?

  1. $\frac{1}{\pi}\int_{0}^{\pi}\sin m\theta \sin n\theta d\theta = 0$
  2. $\frac{1}{2\pi}\int_{-\pi/2}^{\pi /2}\sin p\theta \sin q\theta d\theta = 0$
  3. $\frac{1}{2\pi}\int_{-\pi}^{\pi}\sin p\theta \cos q\theta d\theta = 0$
  4. $\displaystyle \lim_{\alpha\rightarrow \infty }\frac{1}{2\alpha }\int_{-\alpha }^{\alpha }\sin p\theta \sin q\theta d\theta = 0$
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