Question

Prove the following trigonometric identity clearly with steps thanks

Answer 1

Answer:

Let's just use the following basic facts:

 sec x = 1 / cos x

 cos ( π/2 - x ) = sin x

 sin ( π/2 - x ) = cos x

 sin (-x) = -sin x

 tan x = sin x / cos x

Then:

 sec ( x + π/2 ) = 1 / cos ( π/2 + x ) = 1 / cos ( π/2 - (-x) ) = 1 / sin (-x) = -1 / sin x

and

 sin ( x - π/2 ) = -sin ( π/2 - x ) = -cos x

so the whole product is

 sec ( x + π/2 ) sin ( x - π/2 ) tan x

= ( -1/sin x ) ( -cos x ) ( sin x / cos x )

= 1

Hope this helps.