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Popular >

-2cos(x)-4sin(2x)=0

Solution

- 2 cos (x) - 4 sin (2 x) = 0

Solution

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = - 0.25268 \dots + 2 πn, x = π + 0.25268 \dots + 2 πn

+1

Solution steps

- 2 cos (x) - 4 sin (2 x) = 0

Rewrite using trig identities

- 2 cos (x) - 8 cos (x) sin (x) = 0

Factor

- 2 cos (x) - 8 cos (x) sin (x) : - 2 cos (x) (4 sin (x) + 1)

- 2 cos (x) (4 sin (x) + 1) = 0

Solving each part separately

cos (x) = 0 or 4 sin (x) + 1 = 0

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

4 sin (x) + 1 = 0 : x = arcsin (- \frac{1}{4}) + 2 πn, x = π + arcsin (\frac{1}{4}) + 2 πn

Combine all the solutions

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = arcsin (- \frac{1}{4}) + 2 πn, x = π + arcsin (\frac{1}{4}) + 2 πn

Show solutions in decimal form

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = - 0.25268 \dots + 2 πn, x = π + 0.25268 \dots + 2 πn

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sec(x+10)=5.759

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