What is the general solution for picos(pix)+pisin(pix)=0 ?

The general solution for picos(pix)+pisin(pix)=0 is x= 3/4+n

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picos(pix)+pisin(pix)=0

π cos (π x) + π sin (π x) = 0

x = \frac{3}{4} + n

Solution steps

π cos (π x) + π sin (π x) = 0

Rewrite using trig identities

π + π tan (π x) = 0

Move

π

to the right side

π tan (π x) = - π

Divide both sides by

π

tan (π x) = - 1

General solutions for

tan (π x) = - 1

π x = \frac{3 π}{4} + πn

Solve

π x = \frac{3 π}{4} + πn : x = \frac{3}{4} + n

x = \frac{3}{4} + n

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What is the general solution for picos(pix)+pisin(pix)=0 ?
The general solution for picos(pix)+pisin(pix)=0 is x= 3/4+n