Find value of angle theta if …

Given, {tex}\frac { \cos \theta } { 1 - \sin \theta } + \frac { \cos \theta } { 1 + \sin \theta } = 4{/tex}

Taking LCM
 {tex}\frac { \cos \theta ( 1 + \sin \theta ) + \cos \theta ( 1 - \sin \theta ) } { ( 1 - \sin \theta ) ( 1 + \sin \theta ) } = 4{/tex}
 {tex}\frac { \cos \theta [ 1 + \sin \theta + 1 - \sin \theta ] } { 1 - \sin ^ { 2 } \theta } = 4{/tex}
 {tex}\frac { \cos \theta ( 2 ) } { \cos ^ { 2 } \theta } = 4{/tex}
 {tex}\frac { 2 } { \cos \theta } = 4{/tex}
 {tex}\cos \theta = \frac { 2 } { 4 } = \frac { 1 } { 2 }{/tex}
 {tex}\cos \theta = \cos 60 ^ { \circ }{/tex}
{tex}\therefore \theta = 60 ^ { \circ }{/tex}

Given, {tex}\frac { \cos \theta } { 1 - \sin \theta } + \frac { \cos \theta } { 1 + \sin \theta } = 4{/tex}

Taking LCM
 {tex}\frac { \cos \theta ( 1 + \sin \theta ) + \cos \theta ( 1 - \sin \theta ) } { ( 1 - \sin \theta ) ( 1 + \sin \theta ) } = 4{/tex}
 {tex}\frac { \cos \theta [ 1 + \sin \theta + 1 - \sin \theta ] } { 1 - \sin ^ { 2 } \theta } = 4{/tex}
 {tex}\frac { \cos \theta ( 2 ) } { \cos ^ { 2 } \theta } = 4{/tex}
 {tex}\frac { 2 } { \cos \theta } = 4{/tex}
 {tex}\cos \theta = \frac { 2 } { 4 } = \frac { 1 } { 2 }{/tex}
 {tex}\cos \theta = \cos 60 ^ { \circ }{/tex}
{tex}\therefore \theta = 60 ^ { \circ }{/tex}