Question

If sin 2{ (2/1) • (3/2) • (4/3) ••••(x-1)/(x-2)} = 1, 0º < x < 100° then the value of x is equal to:
(A) 91°
(C) 49°
(B) 80°
(D) 46°​

Answer 1

Answer:

Sin2(1/2×2/3×3/4…x-1/x-2)=1 gives

Sin2(1/x-2)=1

Because all the terms will cancel except these two terms

Since 0°<x<100°

Sin2(1/x-2)=Sin(360n+90°)

Which gives

2(1/x-2)=360n+90°

1/x-2=180n+45°

X=(1/180n+45°)+2

X=91/45°for n=0

X=451/225 for n=1

By this way there may be many possible values such as

{X:2<X</=91/40°}