Evaluate $cos 48^{o} - sin 42^{o}$

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Solution

Consider $cos 48^{0}$ which can be rewritten as follows:

$cos 48^{0} = cos {(90^{0} - 42}^{0}) = sin 42^{0} (∵ cos (90^{0} - x) = sin x)$

Therefore, $cos 48^{0} - sin 42^{0}$ can be evaluated as shown below:

$cos 48^{0} - sin 42^{0} = sin 42^{0} - sin 42^{0} = 0$

Hence, $cos 48^{0} - sin 42^{0} = 0$ .

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