What is the general solution for cos^2(x)-sin^2(x)= 1/(sqrt(2)) ?

The general solution for cos^2(x)-sin^2(x)= 1/(sqrt(2)) is x= pi/8+pin,x=(7pi)/8+pin

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cos^2(x)-sin^2(x)= 1/(sqrt(2))

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

x = \frac{π}{8} + πn, x = \frac{7 π}{8} + πn

Solution steps

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

Rewrite using trig identities

cos (2 x) = \frac{1}{2}

Simplify

\frac{1}{2} : \frac{2}{2}

General solutions for

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

2 x = \frac{π}{4} + 2 πn, 2 x = \frac{7 π}{4} + 2 πn

Solve

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

Solve

2 x = \frac{7 π}{4} + 2 πn : x = \frac{7 π}{8} + πn

x = \frac{π}{8} + πn, x = \frac{7 π}{8} + πn

arctan (2 x) + arctan (x) = \frac{π}{2}

sec (\frac{b}{4}) csc (\frac{b}{4}) = 2 csc (\frac{b}{4})

2 cos (x) - 5 = 3 cos (x) - 4

\frac{π}{2} = arctan (x)

cos (n x) = 0

What is the general solution for cos^2(x)-sin^2(x)= 1/(sqrt(2)) ?
The general solution for cos^2(x)-sin^2(x)= 1/(sqrt(2)) is x= pi/8+pin,x=(7pi)/8+pin