If sin 2theta and cos 2theta are solutions of | vedclass

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(B) Given the quadratic equation $x^2 + ax - c = 0$. Since $\sin 2	heta$ and $\cos 2	heta$ are the roots of the equation,we have: Sum of roots: $\si

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$a^2 + 2c - 1 = 0$

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(B) Given the quadratic equation $x^2 + ax - c = 0$. Since $\sin 2	heta$ and $\cos 2	heta$ are the roots of the equation,we have: Sum of roots: $\sin 2	heta + \cos 2	heta = -a$ Product of roots: $\sin 2	heta \cdot \cos 2	heta = -c$ Squaring the sum of roots: $(\sin 2	heta + \cos 2	heta)^2 = (-a)^2$ $\sin^2 2	heta + \cos^2 2	heta + 2 \sin 2	heta \cos 2	heta = a^2$ Using the identity $\sin^2 A + \cos^2 A = 1$: $1 + 2(\sin 2	heta \cos 2	heta) = a^2$ Substitute the product of roots $-c$: $1 + 2(-c) = a^2$ $1 - 2c = a^2$ $a^2 + 2c - 1 = 0$

If $\sin 2\theta$ and $\cos 2\theta$ are solutions of $x^2 + ax - c = 0$,then

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