Question

Sin pi/4 sin pi/6= 1/2(_____ pi/12-cos 5pi/12)

Answer 1

`sin(\pi)/(4)sin(\pi)/(6)=(1)/(2)(cos(\pi)/(12)-cos(5\pi)/(12))`

Explanation:

We are given that

`sin(\pi)/(4) sin(\pi)/(6)`

We have to correct value in blank space.

We know that identity

`sin xsiny=(cos(x-y)-cos(x+y))/(2)`

Using this identity

`sin(\pi)/(4)sin(\pi)/(6)=(cos((\pi)/(4)-(\pi)/(6))-cos((\pi)/(4)+(\pi)/(6)))/(2)`

`sin(\pi)/(4)sin(\pi)/(6)=(cos((3\pi-2\pi)/(12)-cos((3\pi+2\pi)/(12)))/(2)`

`sin(\pi)/(4)sin(\pi)/(6)=(1)/(2)(cos(\pi)/(12)-cos(5\pi)/(12))`

Answer:
`sin(\pi)/(4)sin(\pi)/(6)=(1)/(2)(cos(\pi)/(12)-cos(5\pi)/(12))`