Solve #tan2A=cot(A-18)# #0<theta<90# ?

1 Answer
Nghi N
May 22, 2018

#A = 13.95 + k60^@#

Explanation:

First, convert 18 radians into degrees.
18 radians --> #((180^@)(18))/3.14 = 1031^@85#
tan 2A = cot (A - 18) (1)
Use identity: cot a = tan (90 - a)
Call a = (A - 18)
cot (A - 18) = cot (A - 1031.85) = cot (A - 311.85) =
cot (A - 18) = tan (90 - (A - 311.85)) = tan (401.85 - A)
cot (A - 18) = tan (41.85 - A)
Equation (1) becomes:
#tan 2A = tan (41^@85 - A)#
Unit circle and property of tan function give -->
#2A = 41^@85 - A + k180^@#
#3A = 41^@85 + k180^@#.
#A = 13^@95 + k60^@#
Check with calculator.
k = 1 --> A = 13.95 + 60 = 73.95 --> tan 2A = tan 147.5 = - 0.63
cot (73.95 - 1031.85) = cot (- 237.9 - 720) = - 0.63 . Proved

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