Compute the exact value of #{tan220^\circ-sin220^\circ}/{tan220^\circsin220^\circ}# without a calcuator?

#{tan220^\circ-sin220^\circ}/{tan220^\circsin220^\circ}#enter image source here

1 Answer
Daniel L.
Sep 23, 2017

See explanation.

Explanation:

#(tan220-sin220)/(tan220*sin220)=tan220/(tan220*sin220)-sin220/(tan220*sin220)=#

#1/sin220-1/tan220=1/sin220-cos220/sin220=#

#(1-cos220)/sin220=(1-cos(180+40))/sin(180+40)=#

#(1+cos40)/(-sin40)#

Finding the exact value of the expression is not possible, but we can see that it is negative, so looking at the answers we can mark answer #C#. The value is about #-0.99#

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