Answer:
LHS = RHS
Step-by-step explanation:
[tex] \sec(x) - \cos(x) \\ = \frac{1}{ \cos(x) } - \cos(x) \\ = \frac{1 - { \cos(x) }^{2} }{ \cos(x) } [/tex]
Since
[tex] { \sin(x) }^{2} + { \cos(x) }^{2} = 1 \\ 1 - { \cos(x) }^{2} = { \sin(x) }^{2} [/tex]
Therefore,
[tex] \frac{1 - \ { \cos(x) }^{2} }{ \cos(x) } \\ = \frac{ { \sin(x) }^{2} }{ \cos(x) } \\ = \frac{ \sin(x ) \times \sin(x) }{ \cos(x) } \\ = \sin(x) \tan(x) [/tex]
Therefore LHS = RHS
