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

The general solution for sin(x+pi/2)=-cos(x) is x= pi/2+2pin,x=(3pi)/2+2pin

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

sin (x + \frac{π}{2}) = - cos (x)

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

Solution steps

sin (x + \frac{π}{2}) = - cos (x)

Rewrite using trig identities

cos (x) = - cos (x)

Subtract

- cos (x)

from both sides

2 cos (x) = 0

Divide both sides by

2

cos (x) = 0

General solutions for

cos (x) = 0

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

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

x, sin^{2} (x) = cos^{2} (x)

cos (θ) = 1 + 2 cos (θ)

cos (β) = \frac{2}{7}

tan (x) = \frac{930}{1793}

What is the general solution for sin(x+pi/2)=-cos(x) ?
The general solution for sin(x+pi/2)=-cos(x) is x= pi/2+2pin,x=(3pi)/2+2pin