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

The general solution for 2sin(2x)+cos(2x)=0 is x=-(0.46364…)/2+(pin)/2

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

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

x = - \frac{0.46364 \dots}{2} + \frac{πn}{2}

Solution steps

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

Rewrite using trig identities

2 tan (2 x) + 1 = 0

Move

1

to the right side

2 tan (2 x) = - 1

Divide both sides by

2

tan (2 x) = - \frac{1}{2}

Apply trig inverse properties

2 x = arctan (- \frac{1}{2}) + πn

Solve

2 x = arctan (- \frac{1}{2}) + πn : x = - \frac{arctan ( \frac{1}{2} )}{2} + \frac{πn}{2}

x = - \frac{arctan ( \frac{1}{2} )}{2} + \frac{πn}{2}

Show solutions in decimal form

x = - \frac{0.46364 \dots}{2} + \frac{πn}{2}

sin (2 x + \frac{π}{3}) = 0

300 = \frac{1}{32} 10 0^{2} sin (2 x)

sin^{2} (x) = \frac{45}{52}

2 cos^{2} (x) - 2 sin^{2} (x) = 3

\frac{π ^{2}}{8} sec^{2} (\frac{π x}{4}) tan (\frac{π x}{4}) = 0

What is the general solution for 2sin(2x)+cos(2x)=0 ?
The general solution for 2sin(2x)+cos(2x)=0 is x=-(0.46364…)/2+(pin)/2