What is the general solution for -6sin(t)+6cos(2t)=0 ?

The general solution for -6sin(t)+6cos(2t)=0 is t=(3pi)/2+2pin,t= pi/6+2pin,t=(5pi)/6+2pin

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-6sin(t)+6cos(2t)=0

- 6 sin (t) + 6 cos (2 t) = 0

t = \frac{3 π}{2} + 2 πn, t = \frac{π}{6} + 2 πn, t = \frac{5 π}{6} + 2 πn

Solution steps

- 6 sin (t) + 6 cos (2 t) = 0

Rewrite using trig identities

(1 - 2 sin^{2} (t)) \cdot 6 - 6 sin (t) = 0

Solve by substitution

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

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

sin (t) = \frac{1}{2} : t = \frac{π}{6} + 2 πn, t = \frac{5 π}{6} + 2 πn

Combine all the solutions

t = \frac{3 π}{2} + 2 πn, t = \frac{π}{6} + 2 πn, t = \frac{5 π}{6} + 2 πn

cos^{2} (x) = 4

- 2 tan (θ) - sec (θ) = 0

4 cos (x) = - sin^{2} (x) + 1, 0 \leq x \leq 2 π

2 \cdot sin (x) = tan (x)

0 = arcsin (x)

What is the general solution for -6sin(t)+6cos(2t)=0 ?
The general solution for -6sin(t)+6cos(2t)=0 is t=(3pi)/2+2pin,t= pi/6+2pin,t=(5pi)/6+2pin