Question

Prove the identity. secx- cos x = sin x tan x

Answer 1

Answer:

LHS = RHS

Step-by-step explanation:

$\sec(x) - \cos(x) \\ = \frac{1}{ \cos(x) } - \cos(x) \\ = \frac{1 - { \cos(x) }^{2} }{ \cos(x) }$

Since

${ \sin(x) }^{2} + { \cos(x) }^{2} = 1 \\ 1 - { \cos(x) }^{2} = { \sin(x) }^{2}$

Therefore,

$\frac{1 - \ { \cos(x) }^{2} }{ \cos(x) } \\ = \frac{ { \sin(x) }^{2} }{ \cos(x) } \\ = \frac{ \sin(x ) \times \sin(x) }{ \cos(x) } \\ = \sin(x) \tan(x)$

Therefore LHS = RHS