Question

solve the equation: (1/sqrt2)(sin(x) + cos(x)) = 1 where 0 <= x < 2pi i can't think of any identities to work this problem out

Answer 1

try squaring both sides.

Answer 2

alright after trying that i got it down to sin(2x) = 1 using the double angle formula
but now i don't know how to simplify that

Answer 3

find all angles y such that sin(y)=1

Answer 4

if you look at a table, or a graph of sin, you see y= pi/2 and x = y/2 = pi/4
if we are more careful, y = pi/2 + 2pi*k (k an integer)
and x = pi/4 + pi*k
now check each solution... when we squared the original equation we may (did) introduce extraneous solutions)

Answer 5

yeah i see this now, i appreciate all the help :D