Question

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

Answer 1

LHS = RHS

Explanation:

`\sec(x) - \cos(x) \\ = (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) } \\ = ( \sin(x ) * \sin(x) )/( \cos(x) ) \\ = \sin(x) \tan(x)`

Therefore LHS = RHS