Exams › SSC CGL (Prelims) › General

If \(\cos A + \sin A = \sqrt{2}\cos A\), then \(\cos A - \sin A\) is equal to:

1. \(\sqrt{2}\sin A\)
2. \(\sin A\)
3. 0
4. \(\sqrt{2}\)

Correct answer: \(\sqrt{2}\sin A\)

Solution

From \(\cos A + \sin A = \sqrt{2}\cos A\), we get \(\sin A = (\sqrt{2}-1)\cos A\). Substituting into \(\cos A - \sin A\) and simplifying gives the required expression. The result matches the standard form obtained from the given relation.

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