If \sin x=\sin y and \cos x=\cos y, then the value of x-y is

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Question Id : 11641 | Context :NIMCET 2024

$\sin x=\sin y$ and

$\cos x=\cos y$ , then the value of x-y is

🎥 Video solution / Text Solution of this question is given below:

$\sin x = \sin y \quad \text{and} \quad \cos x = \cos y$

$\sin x = \sin y \Rightarrow x = y + 2n\pi \quad \text{or} \quad x = \pi - y + 2n\pi$

$\cos x = \cos y \Rightarrow x = y + 2m\pi \quad \text{or} \quad x = -y + 2m\pi$

For both $\sin x = \sin y$ and $\cos x = \cos y$ to be true, the only consistent solution is:

$x = y + 2n\pi \Rightarrow x - y = 2n\pi$

$\boxed{x - y = 2n\pi \quad \text{for } n \in \mathbb{Z}}$

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