sin(x)+cos(x)=1.41

Question

cos(x)+sin(x)=1.4142  helppppppp

Answer 1

cos(x)+sin(x)=1.4142

There are two things you have to notice here.

1) 1.4142 is sqrt(2) and cos(pi/4) = sin(pi/4) = 1/sqrt(2)

2) sin(A+B) = sinA.cosB + cosA.sinB

And you can apply both of these observations to the equation you have to solve.

Starting with cos(x)+sin(x)=1.4142

cos(x)*(1/sqrt(2)) + sin(x)*(1/sqrt(2)) = 1

cos(x).sin(pi/4) + sin(x).cos(pi/4) = 1

sin(x+pi/4) = 1 = sin(pi/2)

x+pi/4 = pi/2

x = pi/4