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

1 Answer

4 votes

Answer:


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))

User AxelEckenberger
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