Question

Secx- cosx = sinx tanx

Answer 1

See Explanation

Explanation:

`\sec \: x - cos \: x = \sin \: x \tan \: x \\ \\ LHS = \sec \: x - cos \: x \\ \\ = (1)/( \cos x) - cos \: x \\ \\ = \frac{1 - { \cos x}^(2) }{ \cos x} \\ \\ = \frac{ { \sin x}^(2) }{ \cos x} \\ \\ = ( \sin \: x * \sin x)/( \cos x) \\ \\ = \sin x \: tan x \\ \\ = RHS \\ \\ thus \: proved \\`