Question

If sin A + cos A = `sqrt(2)`, then the value of cos² A is ______.

Options

• `sqrt(2)`

• `1/2`

• 4

• – 1

Answer 1

If sin A + cos A = `sqrt(2)`, then the value of cos² A is `underlinebb(1/2)`.

Explanation:

Given, sin A + cos A = `sqrt(2)`

∴ `1/sqrt(2) sin A + 1/sqrt(2) cos A` = 1

`\implies sin  π/4 sin A + cos A cos  π/4` = 1

`\implies cos(A - π/4)` = 1

`\implies A - π/4` = 0

`\implies` A = `π/4`

Now, cos² A = `cos^2  π/4`

= `(1/sqrt(2))^2`

= `1/2`