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If sin A - √(6)cos A = √(7)cos A, then the value of cos A + √(6)sin A is:

1. √(6)sin A
2. √(7)sin A
3. √(6)cos A
4. √(7)cos A

Correct answer: √(7)sin A

Solution

The equation can be rearranged to isolate terms involving sin A and cos A, leading to a relationship that allows us to express cos A + sqrt{6} sin A in terms of sin A. By substituting and simplifying, we find that it equals sqrt{7} sin A, confirming option B as the correct answer.

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