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If cos t - sin t = sqrt(2)*sin t, then which relation is correct?

1. cos t + sin t = sqrt(2)*cos t
2. cos t + sin t = sqrt(2)*sin t
3. cos t - sin t = sqrt(2)*cos t
4. cos t + sin t = cos t - sin t

Correct answer: cos t + sin t = sqrt(2)*cos t

Solution

Rearranging the hypothesis gives cos t = (sqrt(2) + 1) sin t, and substituting into cos t + sin t shows it equals sqrt(2) cos t.

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