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Popular >

3sec^2(x)-2tan^2(x)-4=0

Solution

3 sec^{2} (x) - 2 tan^{2} (x) - 4 = 0

Solution

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

+1

Solution steps

3 sec^{2} (x) - 2 tan^{2} (x) - 4 = 0

Rewrite using trig identities

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

Solve by substitution

sec (x) = 2, sec (x) = - 2

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

sec (x) = - 2 : x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

Combine all the solutions

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

Popular Examples

2 sin^{2} (2 x) = 1

cos(x)= 1/(sqrt(2))

cos (x) = \frac{1}{2}

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

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

cos (x) = \frac{4}{5}

tan (x) - 1 = 0