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

The general solution for cos(2t)=-sin(t) is t=(7pi)/6+2pin,t=(11pi)/6+2pin,t= pi/2+2pin

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cos(2t)=-sin(t)

cos (2 t) = - sin (t)

t = \frac{7 π}{6} + 2 πn, t = \frac{11 π}{6} + 2 πn, t = \frac{π}{2} + 2 πn

Solution steps

cos (2 t) = - sin (t)

Subtract

- sin (t)

from both sides

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

Rewrite using trig identities

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

Solve by substitution

sin (t) = - \frac{1}{2}, sin (t) = 1

sin (t) = - \frac{1}{2} : t = \frac{7 π}{6} + 2 πn, t = \frac{11 π}{6} + 2 πn

sin (t) = 1 : t = \frac{π}{2} + 2 πn

Combine all the solutions

t = \frac{7 π}{6} + 2 πn, t = \frac{11 π}{6} + 2 πn, t = \frac{π}{2} + 2 πn

sin^{2} (x) - 5 cos (x) - 5 = 0

\frac{1 + tan ^{2} ( 27 \cdot θ )}{1 - tan ^{2} ( 27 \cdot θ )} = 2

tan (x) = - cot (x)

3 cos^{2} (x) - sin^{2} (x) = 0

cos (x) = - 0.6

What is the general solution for cos(2t)=-sin(t) ?
The general solution for cos(2t)=-sin(t) is t=(7pi)/6+2pin,t=(11pi)/6+2pin,t= pi/2+2pin