Question

Tunjukkan bahwa pernyataan berikut benar

( sin x - sin y ) / ( sin x + sin y ) = tan 1/2 ( x-y ) / tan 1/2 ( x + y )

Answer 1

P = sin x - sin y = 2 cos 1/2(x+y) sin 1/2 (x-y)
q = sin x + sin y = 2 sin 1/2 (x+y) cos 1/2(x-y)
.
p/q = 2 cos 1/2 (x+y) sin 1/2(x-y)/ 2 sin 1/2(x+y) cos 1/2(x-y)
bagi dengan cos 1/2(x-y)
p/ cos 1/2(x-y) = 2 cos 1/2(x+y). tan 1/2(x-y)
q/cos 1/2(x-y) = 2 sin 1/2 (x+y)

= 2 cos 1/2 (x+y) . tan1/2(x-y) / 2 sin 1/2(x+y)
= cot 1/2(x+y) . tan 1/2(x-y)
= tan 1/2( x-y) / tan 1/2 (x+y)