Question

Sa se verifice egalitatile pentru x €
a) sin (pi pe 2 +x) = cos
b) cos (pi pe 2+x) =-sin x

Answer 1

a) Folosim formula sin(x+y)=sinxcosy+sinycosx, in care y=$\frac{ \pi }{2}$
Avem: $sin(x+\frac{ \pi }{2})=sinxcos\frac{ \pi }{2}+sin\frac{ \pi }{2}cosx$
Stim [tex]sin\frac{ \pi }{2}=1 [/tex]
$cos\frac{ \pi }{2}=0$
Inlocuind obtinem $sin(x+\frac{ \pi }{2})=cosx$

b) Folosim formula
cos(y+x)=cosycosx-sinysinxx, in care y=$\frac{ \pi }{2}$
Stim [tex]sin\frac{ \pi }{2}=1 [/tex]
$cos\frac{ \pi }{2}=0$
Inlocuind obtinem $cos(\frac{ \pi }{2}+x)=-sinx$