If ` sin A-sqrt6 cos A = sqrt7 cos A , " then " cos A + sqrt6 sin A ` is equal to

Options

A. `sqrt6 sin A `
B. `-sqrt7 sin A `
C. `sqrt6 cos A`
D. `sqrt42 cos A `

Answer

B

Explanation

Given , ` sin A - sqrt6 cos A =sqrt7 cos A`
On squaring given equation we get
` sin^(2) A + 6 cos^(2) A -2 sqrt6 sin A cos A = 7 cos^(2) A`
` Rightarrow sin^(2) A + 6 (1 -sin^(2) A) = cos^(2) A + 6 cos^(2) A+ 2sqrt6 sin A cos A`
` Rightarrow sin^(2) A - 6 cos^(2) A + 6 sin^(2) A + 2sqrt 6 sin A cos A`
` Rightarrow 7 sin^(2) A = ( cos A + sqrt6 sin A)^(2)`
` Rightarrow +-sqrt7 sin A = cos A + sqrt6 sin A `
Alternate Method
Given , `sin A- sqrt6 cos A = sqrt7 cos A `
Replacing A by ` 90^(@) + A,` we get
` sin (90^(@) +A) -sqrt6 cos (90^(@) +A) =sqrt7 cos (90^(@) +A)`
`cos A + sqrt6 A = -sqrt7 sin A `