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

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(A) Given that $\sin A = \sin B$ and $\cos A = \cos B.$Subtracting the squares of the equations:$\sin^2 A + \cos^2 A = \sin^2 B + \cos^2 B$$1 = 1$ (Th

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) Given that $\sin A = \sin B$ and $\cos A = \cos B.$Subtracting the squares of the equations:$\sin^2 A + \cos^2 A = \sin^2 B + \cos^2 B$$1 = 1$ (This is always true).Consider the difference formula:$\cos A = \cos B \Rightarrow \cos A - \cos B = 0$$-2 \sin \frac{A+B}{2} \sin \frac{A-B}{2} = 0$Also,$\sin A = \sin B \Rightarrow \sin A - \sin B = 0$$2 \cos \frac{A+B}{2} \sin \frac{A-B}{2} = 0$From these,we can see that $\sin \frac{A-B}{2} = 0$ must hold for both conditions to be satisfied simultaneously.

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

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