Question #f3dd9

1 Answer
Nghi N.
Jul 18, 2016

#63^@43, and 243^@43#

Explanation:

tan x - sec x = 1
#(sin x)/(cos x) - 1/(cos x) = 1#
#(sin x - cos x)/(cos x) = 1#
sin x - cos x = cos x
sin x - 2cos x = 0
Call t the arc whose tan t = 2 --> #t = 63^@43#
#sin x - ((sin t)/(cos t))cos x = 0#
sin x.cos t - sin t.cos x = sin (x - t)= 0
sin (x - 63.43) = 0
There are 2 solutions for the arc #(x - 63^@43)#
a. x - 63.43 = 0 --> x = 63^@43
b. x - 63.43 = 180 --> x = 180 + 63.43 = 243^@43
Answers for #(0, 2pi):#
#63^@43#, and #243^@43#

Related questions
See all questions in Solving Trigonometric Equations
Impact of this question
1170 views around the world
You can reuse this answer
Creative Commons License