Trigonometry
Solve the following equation for x if x lies in the interval [0,π8)∪(π8,π4]\left[0,\frac{\pi}{8}\right)\cup\left(\frac{\pi}{8},\right.\left.\frac{\pi}{4}\right\rbrack[0,8π)∪(8π,4π] .
y=5+7sec4xy=\sqrt5+7\sec4xy=5+7sec4x
x=14sec−1(y+57)x=\frac14\sec^{-1}\left(\frac{y+\sqrt5}{7}\right)x=41sec−1(7y+5)x=14sec−1(y−57)x=\frac14\sec^{-1}\left(\frac{y-\sqrt5}{7}\right)x=41sec−1(7y−5)
x=4sec−1(y−57)x=4\sec^{-1}\left(\frac{y-\sqrt5}{7}\right)x=4sec−1(7y−5)
x=7sec−1(y−54)x=7\sec^{-1}\left(\frac{y-\sqrt5}{4}\right)x=7sec−1(4y−5)x=14sec−1(y−57)x=\frac14\sec^{-1}\left(\frac{y-\sqrt5}{7}\right)x=41sec−1(7y−5)
x=14sec−1(y−57)x=\frac14\sec^{-1}\left(\frac{y-\sqrt5}{7}\right)x=41sec−1(7y−5)