Question

solve for x: Sqrt(1+cosX) - Sqrt(2)cos(x/2) = Sqrt(2)
the radical 2 is not including cos x/2

Answer 1

@kropot72

Answer 2

@perl would you be able to help me with this?

Answer 3

add sqrt(2)cos(x/2) to both sides

Answer 4

got that, but not sure where to go from there after i square both sides

Answer 5

@perl not seeing how to continue

Answer 6

Sqrt(1+cosX) - Sqrt(2)cos(x/2) = Sqrt(2)

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

square both sides

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

Answer 7

hold on this format is a little confusing

Answer 8

actually theres a simpler way to do this , i think

Answer 9

notice that
sqrt( 1 + cos x) , is very close to sqrt ( (1 + cos x ) / 2)) , which is equal to cos(x/2)

Answer 10

Sqrt(1+cosX) - Sqrt(2)cos(x/2) = Sqrt(2)

divide both sides of equation by sqrt(2)

Answer 11

unfortunately my draw box does not work , i get invisible ink

Answer 12

not seeing how the previous is similar to the latter, is this a rule or something?

Answer 13

there is a trig identity
called half angle identity
http://www.purplemath.com/modules/idents.htm
cos(x/2) = sqrt( (1 + cos x ) / 2)

Answer 14

so our equation has a pretty close expression

Answer 15

watch what happens when you divide both sides by sqrt(2)