cos(x)cot(x)=cos(x)cot(3x-50)

Solution

cos (x) cot (x) = cos (x) cot (3 x - 50)

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = πn + 25, x = \frac{π}{2} + 25 + πn

Solution steps

cos (x) cot (x) = cos (x) cot (3 x - 50)

Subtract

cos (x) cot (3 x - 50)

from both sides

cos (x) cot (x) - cos (x) cot (3 x - 50) = 0

Factor

cos (x) cot (x) - cos (x) cot (3 x - 50) : cos (x) (cot (x) - cot (- 50 + 3 x))

cos (x) (cot (x) - cot (- 50 + 3 x)) = 0

Solving each part separately

cos (x) = 0 or cot (x) - cot (- 50 + 3 x) = 0

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

cot (x) - cot (- 50 + 3 x) = 0 : x = πn + 25, x = \frac{π}{2} + 25 + πn

Combine all the solutions

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = πn + 25, x = \frac{π}{2} + 25 + πn

7 (2 sin^{2} (x) - 1) = 0

cos (a) = \frac{- 3}{2}

2 cos (2 c) = \frac{( 0 ) - ( 0 )}{( π ) - ( - π )}

- 5 cos (2 θ) - 9 sin (θ) + 8 = - sin (θ)

3 + 3 cos (θ) = 3 + 3 sin (θ)