What is the general solution for 2sin(x-pi/4)+sqrt(2)cos(x)=1 ?

The general solution for 2sin(x-pi/4)+sqrt(2)cos(x)=1 is x= pi/4+2pin,x=(3pi)/4+2pin

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2sin(x-pi/4)+sqrt(2)cos(x)=1

2 sin (x - \frac{π}{4}) + 2 cos (x) = 1

x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

Solution steps

2 sin (x - \frac{π}{4}) + 2 cos (x) = 1

Rewrite using trig identities

2 sin (x) = 1

Subtract

1

from both sides

2 sin (x) - 1 = 0

Move

1

to the right side

2 sin (x) = 1

Divide both sides by

2

sin (x) = \frac{2}{2}

General solutions for

sin (x) = \frac{2}{2}

x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

sin^{2} (θ) = 2 cos (θ) + 1

sin (6 x) cos (10 x) - cos (6 x) sin (10 x) = - 0.1

(cos (θ)) (cos (θ) + 1) = 0

5 - tan^{2} (x) = 4, 0^{\circ} \leq x \leq 36 0^{\circ}

- 2 tan (x) + 1 = 23 + 1

What is the general solution for 2sin(x-pi/4)+sqrt(2)cos(x)=1 ?
The general solution for 2sin(x-pi/4)+sqrt(2)cos(x)=1 is x= pi/4+2pin,x=(3pi)/4+2pin