Question

Question #f3dd9

Answer 1

`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`