What is the general solution for cos(t)-cos(2t)=-0.75 ?

The general solution for cos(t)-cos(2t)=-0.75 is t=2.37207…+2pin,t=-2.37207…+2pin

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cos(t)-cos(2t)=-0.75

cos (t) - cos (2 t) = - 0.75

t = 2.37207 \dots + 2 πn, t = - 2.37207 \dots + 2 πn

Solution steps

cos (t) - cos (2 t) = - 0.75

Subtract

- 0.75

from both sides

cos (t) - cos (2 t) + 0.75 = 0

Rewrite using trig identities

1.75 + cos (t) - 2 cos^{2} (t) = 0

Solve by substitution

cos (t) = - \frac{- 1 + 15}{4}, cos (t) = \frac{1 + 15}{4}

cos (t) = - \frac{- 1 + 15}{4} : t = arccos (- \frac{- 1 + 15}{4}) + 2 πn, t = - arccos (- \frac{- 1 + 15}{4}) + 2 πn

cos (t) = \frac{1 + 15}{4} :

No Solution

Combine all the solutions

t = arccos (- \frac{- 1 + 15}{4}) + 2 πn, t = - arccos (- \frac{- 1 + 15}{4}) + 2 πn

Show solutions in decimal form

t = 2.37207 \dots + 2 πn, t = - 2.37207 \dots + 2 πn

2 cos (A) = - 3

4 sin (x) cos (x) = cos (x)

cos (x) = 2 sin (x) cos (x)

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

tan^{2} (4 5^{\circ} + \frac{x}{3}) = 0.58

What is the general solution for cos(t)-cos(2t)=-0.75 ?
The general solution for cos(t)-cos(2t)=-0.75 is t=2.37207…+2pin,t=-2.37207…+2pin