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Popular >

sqrt(3)sin(x)sec(x)=2sin(x)

Solution

3 sin (x) sec (x) = 2 sin (x)

Solution

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

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Solution steps

3 sin (x) sec (x) = 2 sin (x)

Subtract

2 sin (x)

from both sides

3 sin (x) sec (x) - 2 sin (x) = 0

Factor

3 sin (x) sec (x) - 2 sin (x) : sin (x) (3 sec (x) - 2)

sin (x) (3 sec (x) - 2) = 0

Solving each part separately

sin (x) = 0 or 3 sec (x) - 2 = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

3 sec (x) - 2 = 0 : x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Combine all the solutions

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

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