Question

sin3 x*cos5x-sin5x*cos3x=1

Answer 1

sin(3x-5x) = 1
sin(-2x) = 1
sin2x = -1
2x = -π/2 + 2πk
x = -π/4 + πk, k∈Z

Answer 2

$sin3 x*cos5x-sin5x*cos3x=1$
$sin(3 x-5x)=1$
$sin(-2x)=1$
$-sin2x=1$
$sin2x=-1$
$2x=- frac{ pi }{2} +2 pi n,$ $n$ ∈ $Z$
$x=- frac{ pi }{4} + pi n,$ $n$ ∈ $Z$