What is the general solution for sin(4x)+cos(4x)=1 ?

The general solution for sin(4x)+cos(4x)=1 is x=(pin)/2 ,x=(pin)/2+pi/8

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sin(4x)+cos(4x)=1

sin (4 x) + cos (4 x) = 1

x = \frac{πn}{2}, x = \frac{πn}{2} + \frac{π}{8}

Solution steps

sin (4 x) + cos (4 x) = 1

Rewrite using trig identities

2 sin (4 x + \frac{π}{4}) = 1

Divide both sides by

2

sin (4 x + \frac{π}{4}) = \frac{2}{2}

General solutions for

sin (4 x + \frac{π}{4}) = \frac{2}{2}

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

Solve

4 x + \frac{π}{4} = \frac{π}{4} + 2 πn : x = \frac{πn}{2}

Solve

4 x + \frac{π}{4} = \frac{3 π}{4} + 2 πn : x = \frac{πn}{2} + \frac{π}{8}

x = \frac{πn}{2}, x = \frac{πn}{2} + \frac{π}{8}

- 4 cos (x) = - sin^{2} (x) + 4, 0 \leq x \leq 2 π

0 = cos^{2} (\frac{π}{12} t)

sec^{2} (x) + 2 sec (x) + 4 = 0

cos (A) = 0.7865

sin (x) = cos (2 x + 5 1^{\circ})

What is the general solution for sin(4x)+cos(4x)=1 ?
The general solution for sin(4x)+cos(4x)=1 is x=(pin)/2 ,x=(pin)/2+pi/8