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

The general solution for 2cos(t)+sin(2t)=0 is t= pi/2+2pin,t=(3pi)/2+2pin

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

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

t = \frac{π}{2} + 2 πn, t = \frac{3 π}{2} + 2 πn

Solution steps

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

Rewrite using trig identities

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

Factor

2 cos (t) + 2 cos (t) sin (t) : 2 cos (t) (sin (t) + 1)

2 cos (t) (sin (t) + 1) = 0

Solving each part separately

cos (t) = 0 or sin (t) + 1 = 0

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

sin (t) + 1 = 0 : t = \frac{3 π}{2} + 2 πn

Combine all the solutions

t = \frac{π}{2} + 2 πn, t = \frac{3 π}{2} + 2 πn

tan (θ) = cos (θ)

cos (x) = 0.766

cos (x) = \frac{sin ( x )}{2}

sin (θ) = - sin (θ) cos (θ)

cos (x) + 3 sin (x) = 0

What is the general solution for 2cos(t)+sin(2t)=0 ?
The general solution for 2cos(t)+sin(2t)=0 is t= pi/2+2pin,t=(3pi)/2+2pin