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cos(x^2)+sin(x^2)=1

Solution

cos (x^{2}) + sin (x^{2}) = 1

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

Solution steps

cos (x^{2}) + sin (x^{2}) = 1

Rewrite using trig identities

2 sin (x^{2} + \frac{π}{4}) = 1

Divide both sides by

2

sin (x^{2} + \frac{π}{4}) = \frac{2}{2}

General solutions for

sin (x^{2} + \frac{π}{4}) = \frac{2}{2}

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

Solve

x^{2} + \frac{π}{4} = \frac{π}{4} + 2 πn : x = 2 πn, x = - 2 πn

Solve

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

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

cos (\frac{x}{3} - \frac{π}{4}) = \frac{1}{2}

12 sin^{2} (x) + 7 cos (x) - 13 = 0

tan (3 x - π) = 1

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

sin (2 x) cos (x) + cos (2 x) sin (x) = 0