What is the general solution for 9-10cos(2x)=0 ?

The general solution for 9-10cos(2x)=0 is x=(0.45102…)/2+pin,x=pi-(0.45102…)/2+pin

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9-10cos(2x)=0

9 - 10 cos (2 x) = 0

x = \frac{0.45102 \dots}{2} + πn, x = π - \frac{0.45102 \dots}{2} + πn

Solution steps

9 - 10 cos (2 x) = 0

Move

9

to the right side

- 10 cos (2 x) = - 9

Divide both sides by

- 10

cos (2 x) = \frac{9}{10}

Apply trig inverse properties

2 x = arccos (\frac{9}{10}) + 2 πn, 2 x = 2 π - arccos (\frac{9}{10}) + 2 πn

Solve

2 x = arccos (\frac{9}{10}) + 2 πn : x = \frac{arccos ( \frac{9}{10} )}{2} + πn

Solve

2 x = 2 π - arccos (\frac{9}{10}) + 2 πn : x = π - \frac{arccos ( \frac{9}{10} )}{2} + πn

x = \frac{arccos ( \frac{9}{10} )}{2} + πn, x = π - \frac{arccos ( \frac{9}{10} )}{2} + πn

Show solutions in decimal form

x = \frac{0.45102 \dots}{2} + πn, x = π - \frac{0.45102 \dots}{2} + πn

2 cos^{2} (2 x) + 3 cos (2 x) + 1 = 0

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

tan^{2} (2 x) - 3 = 0

tan^{2} (θ) = 2 sec (θ) - 1

5 cosh (x) - 3 sinh (x) = 5

What is the general solution for 9-10cos(2x)=0 ?
The general solution for 9-10cos(2x)=0 is x=(0.45102…)/2+pin,x=pi-(0.45102…)/2+pin