Question
if cosx-sinx=root 2 sinx, then what is the value of cosx+sinx. How
Answers
Reiny
√2sinx + sinx = cosx
sinx(√2+1)= cosx
sinx/cosx = 1/(√2+1)
tanx = 1/(√2+1)
now construct a right-angled triange with sides 1 and √2+1
let the hypotenuse be r
r^2 = 1^2 + (√2+1)^2 = 1 + 2 + 2√2 + 1 = 4 + 2√2
r = √(4+2√2))
cosx + sinx = (√2+1)√(4+2√2) + 1/(√(4+2√2)
= (√2 + 2)/(√(4 + 2√2)
You might want to rationalize this to get a different looking answer.
sinx(√2+1)= cosx
sinx/cosx = 1/(√2+1)
tanx = 1/(√2+1)
now construct a right-angled triange with sides 1 and √2+1
let the hypotenuse be r
r^2 = 1^2 + (√2+1)^2 = 1 + 2 + 2√2 + 1 = 4 + 2√2
r = √(4+2√2))
cosx + sinx = (√2+1)√(4+2√2) + 1/(√(4+2√2)
= (√2 + 2)/(√(4 + 2√2)
You might want to rationalize this to get a different looking answer.