How do you simplify (csc 30° )(tan 60° )?

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Answer 1 · 2015-10-16T10:57:05

#2 cos(30°)/cos(60°)#

Applying the definition:

#csc(30°) tan(60°) = 1/sin(30°)* sin(60°)/cos(60°)#

Since #60# is the double of #30# we can use the double angle formula for #sin(60°)#:

#sin(60°)=sin(2*30°)=2sin(30°)cos(30°)#.

So, we can simplify

#1/cancel(sin(30°))* (2cancel(sin(30°))cos(30°))/cos(60°)#.

So, we've ended up with #2 cos(30°)/cos(60°)#, which I'd say it's no longer possible to simplify.