What is the general solution for (sin(x)+cos(x))^2=2 ?

The general solution for (sin(x)+cos(x))^2=2 is x=2pin+(5pi)/4 ,x=2pin+pi/4

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(sin(x)+cos(x))^2=2

(sin (x) + cos (x))^{2} = 2

x = 2 πn + \frac{5 π}{4}, x = 2 πn + \frac{π}{4}

Solution steps

(sin (x) + cos (x))^{2} = 2

Subtract

2

from both sides

(sin (x) + cos (x))^{2} - 2 = 0

Factor

(sin (x) + cos (x))^{2} - 2 : (sin (x) + cos (x) + 2) (sin (x) + cos (x) - 2)

(sin (x) + cos (x) + 2) (sin (x) + cos (x) - 2) = 0

Solving each part separately

sin (x) + cos (x) + 2 = 0 or sin (x) + cos (x) - 2 = 0

sin (x) + cos (x) + 2 = 0 : x = 2 πn + \frac{5 π}{4}

sin (x) + cos (x) - 2 = 0 : x = 2 πn + \frac{π}{4}

Combine all the solutions

x = 2 πn + \frac{5 π}{4}, x = 2 πn + \frac{π}{4}

tan (θ) = \frac{3}{3}, 18 0^{\circ} \leq θ \leq 36 0^{\circ}

7.5 = 5 sin (\frac{π}{2} (x - 2)) + 5

u, y = ccos h \cdot sin (u)

2 cos (θ) + 23 = 3

- 22 = - 4 sin (2 θ)

What is the general solution for (sin(x)+cos(x))^2=2 ?
The general solution for (sin(x)+cos(x))^2=2 is x=2pin+(5pi)/4 ,x=2pin+pi/4