)
cosx=b/c" "color(blue)((1))
sinx=a/c" "color(blue)((2))
Given that,
sinx+cosx=sqrt2" "color(blue)((3))
Substitute " "color(blue)((1)) and color(blue)((2)) in " "color(blue)((3))
a/c+b/c=sqrt2=>(a+b)/c=sqrt2
a+b=csqrt2
squaring on both sides
(a+b)^2=(csqrt(2))^2=>(a+b)^2=2c^2
a^2+b^2+2ab=2c^2
c^2+2ab=2c^2[since from Pythagoras]
c^2=2ab
a^2+b^2=2ab[since from Pythagoras]
a^2+b^2-2ab=0
(a-b)^2=0
a-b=0
a=b" "color(blue)((4))
equation" "color(blue)((4)) substitute in" "color(blue)((1))
cos x=a/c" "color(blue)((5))
From" "color(blue)((5))&" "color(blue)((2))
cosx=sinx
sin(pi/2-x)=sinx
cancel(sin)(pi/2-x)=cancel(sin)x
pi/2-x=x=>2x=pi/2
x=pi/4radians
or
x=45^@
