Question

3cosø+4sinø=A sin(ø+∆) find value of "A" and "∆"

Answer 1

my keyboard has no theta so I use @ in place of theta ,okay !

now,
3cos@+4sin@=root (3^2+4^2){3/roo(3^2+4^2) cos@ +4/root (3^2+4^2).sin@}

=5{3/5cos@ + 4/5.sin@}
=5{sinx.cos@ +cosx.sin@}
=5sin (x+@)

sinx=3/5 and cosx =4/5
so,
x=tan^-1(3/4 )

hence A=5 and delta = tan^-1 (3/4)
if x in sine term then
x=sin^-1 (3/5)
then delta =sin^-1 (3/5)
option (b) is correct