What is the general solution for 2cos(pi/4-x)=1 ?

The general solution for 2cos(pi/4-x)=1 is x=-2pin-pi/(12),x=-2pin-(17pi)/(12)

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2cos(pi/4-x)=1

2 cos (\frac{π}{4} - x) = 1

x = - 2 πn - \frac{π}{12}, x = - 2 πn - \frac{17 π}{12}

Solution steps

2 cos (\frac{π}{4} - x) = 1

Divide both sides by

2

cos (\frac{π}{4} - x) = \frac{1}{2}

General solutions for

cos (\frac{π}{4} - x) = \frac{1}{2}

\frac{π}{4} - x = \frac{π}{3} + 2 πn, \frac{π}{4} - x = \frac{5 π}{3} + 2 πn

Solve

\frac{π}{4} - x = \frac{π}{3} + 2 πn : x = - 2 πn - \frac{π}{12}

Solve

\frac{π}{4} - x = \frac{5 π}{3} + 2 πn : x = - 2 πn - \frac{17 π}{12}

x = - 2 πn - \frac{π}{12}, x = - 2 πn - \frac{17 π}{12}

sin (θ) = \frac{56}{65}

900 = 400 sin (\frac{2 π t}{365} + \frac{7 π}{8}) + 500

2 sin^{2} (x) + 2 sin (x) = 0

2 sin^{2} (x) = sin (x) + 1, 0 \leq x \leq 2 π

15 tan (θ) - 7 = 5 tan (θ) - 3

What is the general solution for 2cos(pi/4-x)=1 ?
The general solution for 2cos(pi/4-x)=1 is x=-2pin-pi/(12),x=-2pin-(17pi)/(12)