SOLUTION: Evaluate. tan(2 arc tan of 5/12) arc cos(sin of 11pi/6) sin(1/2 arc tan of 24/7)

Question 636488: Evaluate.
tan(2 arc tan of 5/12)
arc cos(sin of 11pi/6)
sin(1/2 arc tan of 24/7)
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Evaluate.
tan(2 arc tan of 5/12)
identity: tan 2x=(2 tanx)/(1-tan^2x)
tan x=5/12
tan(2 arc tan of 5/12)
=(2*(5/12))/(1-(5/12)^2)
=(10/12)/1-(25/144)
=(120/144)/)119/144=120/119
..
arc cos(sin of 11pi/6)
sin 11pi/6=sin 5π/6=.5
arc cos(sin of 11pi/6)
arc cos(.5)
=-√3/2
..
sin(1/2 arc tan of 24/7)
Identity: sin x/2=�√[(1-cos x)/2]
tan x=24/7=opp side/adj side
hypotenuse=√opp side^2+adj side^2)=√(24^2+7^2)=√576+49=√625=25
hypotenuse=25
cos x=adj side/hypotenuse=7/25
sin(1/2 arc tan of 24/7)
=√[(1-cos x)/2]
=√[(1-7/25)/2]
=√[(18/25)/2]
=√18/50
=√(9/25)
=3/5
=0.6
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