Question

Sin {nπ+(-1)^n ×π/4} .....where's n is a complete number ...find the value

Answer 1

sinx=sina
then solution of trigonometry
x=n.pi +(-1)^n(a)

now ,
here given ,
sin {n.pi +(-1)^n (pi/4)}

=sin {pi/4}=1/root2


2nd method :-

sin {n.pi +(-1)^npi/4}
put n=0
sin pi/4= 1/root2
put n=1
sin {pi-pi/4}
=sin3pi/4
sine is positive in second quadrant
so,
sin3pi/4 =1/root2

put n=-1
sin {-pi-pi/4}
=-sin (-pi/4 )=1/root2

hence always we find 1/root2 so, answer is 1/root2