What is the general solution for cos(x+60)*cos(x-60)= 1/2 ?

The general solution for cos(x+60)*cos(x-60)= 1/2 is x=(1.38389…)/2+pin,x=pi-(1.38389…)/2+pin

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cos(x+60)*cos(x-60)= 1/2

cos (x + 60) \cdot cos (x - 60) = \frac{1}{2}

x = \frac{1.38389 \dots}{2} + πn, x = π - \frac{1.38389 \dots}{2} + πn

Solution steps

cos (x + 60) cos (x - 60) = \frac{1}{2}

Subtract

\frac{1}{2}

from both sides

cos (x + 60) cos (x - 60) - \frac{1}{2} = 0

Simplify

cos (x + 60) cos (x - 60) - \frac{1}{2} : \frac{2 cos ( x + 60 ) cos ( x - 60 ) - 1}{2}

\frac{2 cos ( x + 60 ) cos ( x - 60 ) - 1}{2} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

2 cos (x + 60) cos (x - 60) - 1 = 0

Rewrite using trig identities

- 1 + cos (120) + cos (2 x) = 0

Move

1

to the right side

cos (120) + cos (2 x) = 1

Move

cos (120)

to the right side

cos (2 x) = 1 - cos (120)

Apply trig inverse properties

2 x = arccos (1 - cos (120)) + 2 πn, 2 x = 2 π - arccos (1 - cos (120)) + 2 πn

Solve

2 x = arccos (1 - cos (120)) + 2 πn : x = \frac{arccos ( 1 - cos ( 120 ) )}{2} + πn

Solve

2 x = 2 π - arccos (1 - cos (120)) + 2 πn : x = π - \frac{arccos ( 1 - cos ( 120 ) )}{2} + πn

x = \frac{arccos ( 1 - cos ( 120 ) )}{2} + πn, x = π - \frac{arccos ( 1 - cos ( 120 ) )}{2} + πn

Show solutions in decimal form

x = \frac{1.38389 \dots}{2} + πn, x = π - \frac{1.38389 \dots}{2} + πn

\frac{cos ( 2 x + 9 )}{3} = \frac{1}{2}

sin^{6} (x) - cos^{6} (x) = 0

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

sin (2 x) + cos (2 x) - 1 = 0

4 tan (x) sin^{2} (x) + 3 = 4 sin^{2} (x) + 3 tan (x)

What is the general solution for cos(x+60)*cos(x-60)= 1/2 ?
The general solution for cos(x+60)*cos(x-60)= 1/2 is x=(1.38389…)/2+pin,x=pi-(1.38389…)/2+pin