What will be the value of $\frac{sin 30° sin 40° sin 50° sin 60°}{cos30° cos40°cos50°cos60°}$?

1

we know ,

sinA = cos ( 90° - A )

\(\frac{sin 30° . sin40° . sin50° . sin60° }{cos 30° . cos40° . cos50° . cos60° }\)

= \(\frac{ cos ( 90° - 30° ) . cos ( 90° - 40° ) . cos ( 90° - 50° ) . cos ( 90° - 60° ) }{cos 30° . cos40° . cos50° . cos60° }\)

= \(\frac{cos60° . cos50° . cos40° . cos30° }{cos 30° . cos40° . cos50° . cos60° }\)

= 1