Question

Given the angle x construct the angle y if sin y=2sin x

Answer 1

if we are given angle x, andle y is sin y which is equal to 2sin x. upon my understanding angle y will be 45 degree

Answer 2

siny = 2sinx
siny/sinx = 2
use componendo or dividendo rule ,

(siny + sinx)/(siny - sinx) = (2 + 1)/(2 -1)
tan(x+y)/2.cot(x-y)/2 = 3
tan(x + y)/2 = 3tan(x - y)/2

Let tan(x + y)/2 = tanπ/3
and tan(x - y)/2 = tanπ/6
(x + y) = 2π/3 ________(1)
(x - y) = π/3___________(2)
solve it
then, x = π/2 and y = π/6
hence, one solution if it is
( π/2 , π/6)

but general solutions of these are
y = 2nπ ± sin-¹(2sinx)