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2sqrt((2))cos(x-4)sin(x)cos(x)=0

Solution

2 (2) cos (x - 4) sin (x) cos (x) = 0

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

Degrees

x = 319.18311 \dots^{\circ} + 36 0^{\circ} n, x = 499.18311 \dots^{\circ} + 36 0^{\circ} n, x = 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n, x = 9 0^{\circ} + 36 0^{\circ} n, x = 27 0^{\circ} + 36 0^{\circ} n

Solution steps

2 (2) cos (x - 4) sin (x) cos (x) = 0

Solving each part separately

cos (x - 4) = 0 or sin (x) = 0 or cos (x) = 0

cos (x - 4) = 0 : x = \frac{π}{2} + 2 πn + 4, x = \frac{3 π}{2} + 2 πn + 4

cos (x - 4) = 0

General solutions for

cos (x - 4) = 0

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

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

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

Solve

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

x - 4 = \frac{π}{2} + 2 πn

Move

4

to the right side

x - 4 = \frac{π}{2} + 2 πn

Add

4

to both sides

x - 4 + 4 = \frac{π}{2} + 2 πn + 4

Simplify

x = \frac{π}{2} + 2 πn + 4

x = \frac{π}{2} + 2 πn + 4

Solve

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

x - 4 = \frac{3 π}{2} + 2 πn

Move

4

to the right side

x - 4 = \frac{3 π}{2} + 2 πn

Add

4

to both sides

x - 4 + 4 = \frac{3 π}{2} + 2 πn + 4

Simplify

x = \frac{3 π}{2} + 2 πn + 4

x = \frac{3 π}{2} + 2 πn + 4

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

sin (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) = 0

General solutions for

sin (x) = 0

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

x = 0 + 2 πn, x = π + 2 πn

x = 0 + 2 πn, x = π + 2 πn

Solve

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn, x = π + 2 πn

cos (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

cos (x) = 0

General solutions for

cos (x) = 0

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

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

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

Combine all the solutions

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

cos (x) (tan (x) - 3) = 0

2 + 2 cos (t) = 6 cos (t)

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

sin (\frac{( 60 )}{7}) = sin (\frac{( 81 )}{a})

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