What is the general solution for 2sin(x)+cos(2x)=0 ?

The general solution for 2sin(x)+cos(2x)=0 is x=-0.37473…+2pin,x=pi+0.37473…+2pin

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2sin(x)+cos(2x)=0

2 sin (x) + cos (2 x) = 0

x = - 0.37473 \dots + 2 πn, x = π + 0.37473 \dots + 2 πn

Solution steps

2 sin (x) + cos (2 x) = 0

Rewrite using trig identities

1 + 2 sin (x) - 2 sin^{2} (x) = 0

Solve by substitution

sin (x) = - \frac{- 1 + 3}{2}, sin (x) = \frac{1 + 3}{2}

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

sin (x) = \frac{1 + 3}{2} :

No Solution

Combine all the solutions

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

Show solutions in decimal form

x = - 0.37473 \dots + 2 πn, x = π + 0.37473 \dots + 2 πn

2 cosh^{2} (x) - 3 sinh (x) = 1

3 cos^{2} (θ) - sin^{2} (θ) = 2

x, y = \frac{4}{π} arccos (\frac{x}{4})

tan (θ) = \frac{2}{1.5}

tan (x) + 3 = 0, 0 \leq x \leq 2 π

What is the general solution for 2sin(x)+cos(2x)=0 ?
The general solution for 2sin(x)+cos(2x)=0 is x=-0.37473…+2pin,x=pi+0.37473…+2pin