If $\sin A$ and $\cos A$ are roots of the equation $px^2 +rx+m=0$, then the reaction among p, q and m is :

If sin A and cos A are the roots of px^2 + rx + m = 0, then their sum equals -r/p and their product equals m/p. Squaring the sum gives the identity sin^2 A + cos^2 A + 2 sin A cos A = r^2/p^2. Replacing sin^2 A + cos^2 A with 1 and substituting the product m/p yields 1 + 2m/p = r^2/p^2. Multiplying by p^2 gives p^2 + 2mp = r^2, and moving terms around gives r^2 + m^2 = p^2 + 2mp + m^2, which factors to r^2 + m^2 = (p + m)^2.

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