If `sinA+cosA=sqrt(2),` then the value of `cos^(2)` A is

Options

A. `sqrt(2)`
B. `1//2`
C. 4
D. `-1`

Answer

B

Explanation

Given , sin A cos A `=sqrt(2)`
`therefore(1)/(sqrt(2))sinA+(1)/(sqrt(2))cosA=1`
`rArr"sin"(pi)/(4)sinA+cosA"cos"(pi)/(4)=1`
`rArrcos(A-(pi)/(4))=1rArrA-(pi)/(4)=0rArrA=(pi)/(4)`
Now , `cos^(2)A="cos"^(2)(pi)/(4)=((1)/(sqrt(2)))^(2)=(1)/(2)`