If sin A = sin B and cos A = cos B, then | vedclass

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Question

(A) Given that $\sin A = \sin B$ and $\cos A = \cos B$. Squaring both equations and adding them: $\sin^2 A + \cos^2 A = \sin^2 B + \cos^2 B$ $1 = 1$ (

Vedclass · Accepted Answer

$\sin \frac{A - B}{2} = 0$

Vedclass · Answer

(A) Given that $\sin A = \sin B$ and $\cos A = \cos B$. Squaring both equations and adding them: $\sin^2 A + \cos^2 A = \sin^2 B + \cos^2 B$ $1 = 1$ (This is always true). Alternatively,consider $\cos A = \cos B$ and $\sin A = \sin B$. Subtracting the equations: $\cos A - \cos B = 0$ and $\sin A - \sin B = 0$. Using sum-to-product formulas: $-2 \sin \frac{A+B}{2} \sin \frac{A-B}{2} = 0$ $2 \cos \frac{A+B}{2} \sin \frac{A-B}{2} = 0$ For both to be zero,$\sin \frac{A-B}{2}$ must be $0$.

If $\sin A = \sin B$ and $\cos A = \cos B,$ then

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