What is the general solution for cos(pi/4-x)= 12/13 ?

The general solution for cos(pi/4-x)= 12/13 is x=-2pin+pi/4-0.39479…,x=-2pi-2pin+pi/4+0.39479…

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cos(pi/4-x)= 12/13

cos (\frac{π}{4} - x) = \frac{12}{13}

x = - 2 πn + \frac{π}{4} - 0.39479 \dots, x = - 2 π - 2 πn + \frac{π}{4} + 0.39479 \dots

Solution steps

cos (\frac{π}{4} - x) = \frac{12}{13}

Apply trig inverse properties

\frac{π}{4} - x = arccos (\frac{12}{13}) + 2 πn, \frac{π}{4} - x = 2 π - arccos (\frac{12}{13}) + 2 πn

Solve

\frac{π}{4} - x = arccos (\frac{12}{13}) + 2 πn : x = - 2 πn + \frac{π}{4} - arccos (\frac{12}{13})

Solve

\frac{π}{4} - x = 2 π - arccos (\frac{12}{13}) + 2 πn : x = - 2 π - 2 πn + \frac{π}{4} + arccos (\frac{12}{13})

x = - 2 πn + \frac{π}{4} - arccos (\frac{12}{13}), x = - 2 π - 2 πn + \frac{π}{4} + arccos (\frac{12}{13})

Show solutions in decimal form

x = - 2 πn + \frac{π}{4} - 0.39479 \dots, x = - 2 π - 2 πn + \frac{π}{4} + 0.39479 \dots

x, y = f cos (x)

3 cot (2 x) = - 1, 0 \leq x \leq π

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

(cot (θ) - 1) (2 sin (θ) + 3) = 0

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

What is the general solution for cos(pi/4-x)= 12/13 ?
The general solution for cos(pi/4-x)= 12/13 is x=-2pin+pi/4-0.39479…,x=-2pi-2pin+pi/4+0.39479…