sin(x)+cos(x)=a

Solution

sin (x) + cos (x) = a

x = arcsin (\frac{a}{2}) + 2 πn - \frac{π}{4}, x = π + arcsin (- \frac{a}{2}) + 2 πn - \frac{π}{4}

Solution steps

sin (x) + cos (x) = a

Rewrite using trig identities

2 sin (x + \frac{π}{4}) = a

Divide both sides by

2

sin (x + \frac{π}{4}) = \frac{2 a}{2}

Apply trig inverse properties

x + \frac{π}{4} = arcsin (\frac{2 a}{2}) + 2 πn, x + \frac{π}{4} = π + arcsin (- \frac{2 a}{2}) + 2 πn

Solve

x + \frac{π}{4} = arcsin (\frac{2 a}{2}) + 2 πn : x = arcsin (\frac{a}{2}) + 2 πn - \frac{π}{4}

Solve

x + \frac{π}{4} = π + arcsin (- \frac{2 a}{2}) + 2 πn : x = π + arcsin (- \frac{a}{2}) + 2 πn - \frac{π}{4}

x = arcsin (\frac{a}{2}) + 2 πn - \frac{π}{4}, x = π + arcsin (- \frac{a}{2}) + 2 πn - \frac{π}{4}

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

tan (x) - \frac{3}{3} = 0

tan (2 θ) = 0.5714

\frac{3}{1 + cos ( θ )} = 1 + 2 cos (θ)

4 - 4 cos (θ) = 6