Question

sin( pi\4 + x) - cos (pi\4 -x)=0 trebuie sa se demonstreze

Answer 1

sin(pi/4)*cosx+sinx*cos(pi/4)-[cos(pi/4)*cosx+sin(pi/4)*cosx]=0
√2/2*cosx+√2/2*cosx-(√2/2*cosx+√2/2*cosx)=0
Schimbam semnul a ceea ce este in paranteza, se simplifica si da 0
=> 0=0 (A)

Answer 2

sin( pi\4 + x) - cos (pi\4 -x)=
sin(π/4+x)-sin(π/2-(π/4-x))= sin (π/4+x)-sin(π/2-π/4+x)=
sin (π/4+x)-sin (π/4+x)=

sinα-sinα=0
as simple as that!!!