Question

If `sin A - sqrt(6) cos A = sqrt(7) cos A`, then `cos A + sqrt(6) sin A` is equal to ______.

Options

• `sqrt(6) sin A`

• `-sqrt(7) sin A`

• `sqrt(6) cos A`

• `sqrt(42) cos A`

Answer 1

If `sin A - sqrt(6) cos A = sqrt(7) cos A`, then `cos A + sqrt(6) sin A` is equal to `underlinebb(-sqrt(7) sin A)`.

Explanation:

Given, `sin A - sqrt(6) cos A = sqrt(7) cos A`

Replacing A by 90° + A, we get

`sin(90^circ + A) - sqrt(6) cos(90^circ + A) = sqrt(7) cos(90^circ + A)`

`\implies cos A + sqrt(6) sin A = -sqrt(7) sin A`