What is the general solution for cos(2x)= 7/25 ?

The general solution for cos(2x)= 7/25 is x=(1.28700…)/2+pin,x=pi-(1.28700…)/2+pin

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cos(2x)= 7/25

cos (2 x) = \frac{7}{25}

x = \frac{1.28700 \dots}{2} + πn, x = π - \frac{1.28700 \dots}{2} + πn

Solution steps

cos (2 x) = \frac{7}{25}

Apply trig inverse properties

2 x = arccos (\frac{7}{25}) + 2 πn, 2 x = 2 π - arccos (\frac{7}{25}) + 2 πn

Solve

2 x = arccos (\frac{7}{25}) + 2 πn : x = \frac{arccos ( \frac{7}{25} )}{2} + πn

Solve

2 x = 2 π - arccos (\frac{7}{25}) + 2 πn : x = π - \frac{arccos ( \frac{7}{25} )}{2} + πn

x = \frac{arccos ( \frac{7}{25} )}{2} + πn, x = π - \frac{arccos ( \frac{7}{25} )}{2} + πn

Show solutions in decimal form

x = \frac{1.28700 \dots}{2} + πn, x = π - \frac{1.28700 \dots}{2} + πn

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

sin (2 θ) = \frac{a}{5}

cos (a) = - \frac{1}{4}

\frac{cos ^{2} ( x ) - 4}{cos ( x ) - 2} = 1

- 8 sec^{2} (x) - 26 tan (x) = 12

What is the general solution for cos(2x)= 7/25 ?
The general solution for cos(2x)= 7/25 is x=(1.28700…)/2+pin,x=pi-(1.28700…)/2+pin