tan(2sqrt(x)-3)=-1

Solution

tan (2 x - 3) = - 1

x = \frac{9}{4} + \frac{9 π}{8} + \frac{9 π ^{2}}{64} + \frac{3 πn}{2} + \frac{3 π ^{2} n}{8} + \frac{π ^{2} n ^{2}}{4}

Solution steps

tan (2 x - 3) = - 1

General solutions for

tan (2 x - 3) = - 1

2 x - 3 = \frac{3 π}{4} + πn

Solve

2 x - 3 = \frac{3 π}{4} + πn : x = \frac{9}{4} + \frac{9 π}{8} + \frac{9 π ^{2}}{64} + \frac{3 πn}{2} + \frac{3 π ^{2} n}{8} + \frac{π ^{2} n ^{2}}{4} {n > - \frac{96 π + 24 π ^{2}}{32 π ^{2}}}

x = \frac{9}{4} + \frac{9 π}{8} + \frac{9 π ^{2}}{64} + \frac{3 πn}{2} + \frac{3 π ^{2} n}{8} + \frac{π ^{2} n ^{2}}{4}

2 sin^{2} (x) + 5 cos (x) - 3 = 0

3 cos^{2} (x) + 4 cos (x) - 4 = 0

sin (θ) = - \frac{27}{190}

4 sin (θ) = 1 + sin (θ)

tan (θ) - 3 = 0, 0 \leq θ \leq 2 π