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Popular >

3sec(x)-4cos(x)=0

Solution

3 sec (x) - 4 cos (x) = 0

Solution

x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn

+1

Solution steps

3 sec (x) - 4 cos (x) = 0

Rewrite using trig identities

- \frac{4}{sec ( x )} + 3 sec (x) = 0

Solve by substitution

sec (x) = \frac{2 3}{3}, sec (x) = - \frac{2 3}{3}

sec (x) = \frac{2 3}{3} : x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

sec (x) = - \frac{2 3}{3} : x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn

Combine all the solutions

x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn

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