tan(x)csc^2(x)-2tan(x)=0

Solution

tan (x) csc^{2} (x) - 2 tan (x) = 0

x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn, x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

Solution steps

tan (x) csc^{2} (x) - 2 tan (x) = 0

Factor

tan (x) csc^{2} (x) - 2 tan (x) : tan (x) (csc (x) + 2) (csc (x) - 2)

tan (x) (csc (x) + 2) (csc (x) - 2) = 0

Solving each part separately

tan (x) = 0 or csc (x) + 2 = 0 or csc (x) - 2 = 0

tan (x) = 0 : x = πn

csc (x) + 2 = 0 : x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

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

Combine all the solutions

x = πn, x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn, x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

Since the equation is undefined for:

πn

x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn, x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

5 sin (2 x) = cos (x)

2 sin (x + \frac{π}{3}) = - 1

cot^{2} (a) = cos^{2} (a) + cos (a) cos (a)

cot (x) \cdot tan (2 x) = 3

1 \cdot sin (3 5^{\circ}) = 1.33 \cdot sin (θ)