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

The general solution for cos(2x)+cos(pi/2-2x)=-sqrt(2) is x=(5pi)/8+pin

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cos(2x)+cos(pi/2-2x)=-sqrt(2)

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

x = \frac{5 π}{8} + πn

Solution steps

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

Rewrite using trig identities

2 cos (\frac{8 x - π}{4}) = - 2

Divide both sides by

2

cos (\frac{8 x - π}{4}) = - 1

General solutions for

cos (\frac{8 x - π}{4}) = - 1

\frac{8 x - π}{4} = π + 2 πn

Solve

\frac{8 x - π}{4} = π + 2 πn : x = \frac{5 π}{8} + πn

x = \frac{5 π}{8} + πn

cos^{2} (x) = - 1.5

2 arctan (\frac{1}{2}) - arctan (x) = \frac{π}{4}

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

sin (θ) = \frac{13}{85}

sin (2 x) = \frac{( 6 m - 5 )}{8}

What is the general solution for cos(2x)+cos(pi/2-2x)=-sqrt(2) ?
The general solution for cos(2x)+cos(pi/2-2x)=-sqrt(2) is x=(5pi)/8+pin