What is the principal value of angle A? 2tan A= -sec^2 A

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2tan A= -sec^2 A

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Answer 1 · 2018-05-18T02:08:01

#color(indigo)(hat A = n pi - pi/4, n = 1 in ZZ#

#2tan A = -sec^2 A#

#sec ^2 A + 2tan A = 0#

#1 + tan^2 A + 2 tan A = 0#, using identity #1 + tan^2 x = sec^2 x#

#(1 + tan A)^2 = 0#

#1 + tan A = 0#

#tan A = -1#

#hat A = -45^@ = -pi/4#

#color(indigo)(hat A = n pi - pi/4, n = 1 in ZZ#