If sin alpha = sin beta and cos alpha = cos b | vedclass

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(D) Given that $\sin \alpha = \sin \beta$ and $\cos \alpha = \cos \beta$. Squaring and adding both equations: $(\sin \alpha)^2 + (\cos \alpha)^2 = (\s

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$2 n \pi$

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(D) Given that $\sin \alpha = \sin \beta$ and $\cos \alpha = \cos \beta$. Squaring and adding both equations: $(\sin \alpha)^2 + (\cos \alpha)^2 = (\sin \beta)^2 + (\cos \beta)^2$ $1 = 1$. Alternatively,consider the complex numbers $z_1 = \cos \alpha + i \sin \alpha$ and $z_2 = \cos \beta + i \sin \beta$. Since $\cos \alpha = \cos \beta$ and $\sin \alpha = \sin \beta$,we have $z_1 = z_2$. This implies $e^{i \alpha} = e^{i \beta}$,which means $e^{i(\alpha - \beta)} = 1$. Therefore,$\alpha - \beta = 2 n \pi$ for some integer $n$. Hence,option $D$ is correct.

If $\sin \alpha = \sin \beta$ and $\cos \alpha = \cos \beta$,then $\alpha - \beta = $ for some integer $n$.

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