[tex] \frac{1 + \sin(y) }{ \cos(y) } + \frac{ \cos(y) }{1 + \sin(y) } [/tex]
[tex] = \frac{(1 + \sin(y))(1 + \sin(y)) + (\cos(y)) (\cos(y))}{(1 + \sin(y)) (\cos(y)) } [/tex]
[tex] = \frac{ {(1 + \sin(y))}^{2} + {(\cos(y))}^{2} }{(1 + \sin(y))( \cos(y))} [/tex]
[tex] = \frac{1 + 2 \sin(y) + { \sin }^{2} (y) + { \cos}^{2}(y) }{(1 + \sin(y))( \cos(y))} [/tex]
INGAT : [tex] { \sin }^{2}(y) + {\cos}^{2}(y) = 1[/tex]
MAKA :
[tex] = \frac{1 + 2 \sin(y) + 1 }{(1 + \sin(y))( \cos(y))} [/tex]
[tex] = \frac{2 + 2 \sin(y) }{(1 + \sin(y))( \cos(y))} [/tex]
[tex] = \frac{2(1 + \sin(y)) }{(1 + \sin(y))( \cos(y))} [/tex]
[tex] = \frac{2}{ \cos(y) } [/tex]
[tex] = 2 \times \frac{1}{ \cos(y) } [/tex]
INGAT : [tex] \frac{1}{ \cos(y) } = \sec(y) [/tex]
MAKA :
[tex] = 2 \times \sec(y) = 2 \sec(y) [/tex]
TERBUKTI BENAR, BAHWA :
[tex]\frac{1 + \sin(y) }{ \cos(y) } + \frac{ \cos(y) }{1 + \sin(y) } = 2 \sec(y) [/tex]
[answer.2.content]
