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

The general solution for cos(x-pi/4)=-sin(x) is x=-(pi+8pin)/8

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cos(x-pi/4)=-sin(x)

cos (x - \frac{π}{4}) = - sin (x)

x = - \frac{π + 8 πn}{8}

Solution steps

cos (x - \frac{π}{4}) = - sin (x)

Rewrite using trig identities

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

Apply trig inverse properties

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

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

True for all

x; 0 = 2 πn + \frac{3 π}{4}

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

Since the equation is undefined for:

True for all

x

x = - \frac{π + 8 πn}{8}

sin (x) = \frac{5}{13}, cos (x)

tan (θ) = \frac{11.9}{10}

tanh (x) = \frac{3}{5}

csc (θ) + 2.402 = 0

tan^{2} (β) = 1

What is the general solution for cos(x-pi/4)=-sin(x) ?
The general solution for cos(x-pi/4)=-sin(x) is x=-(pi+8pin)/8