Simple trigonometric simplification

[Krushnaraj Pandya]

Homework Statement

Show that sec(x-(pi/2))+tan(x-(pi/2))=tan((x/2)+pi/12))

The Attempt at a Solution

I applied all sorts of half angle formulas to convert it in terms of tan, I got LHS as (tan((x/2)-(pi/6))+1)^2/1-tan^2(x/2-(pi/6)) but I'm sure there must be a simple easy method to get the RHS (PS this is part of a bigger problem, I got the answer as LHS, I need to equate it to RHS for my answer to be correct

 

[Ray Vickson]

Homework Statement

Show that sec(x-(pi/2))+tan(x-(pi/2))=tan((x/2)+pi/12))

The Attempt at a Solution

I applied all sorts of half angle formulas to convert it in terms of tan, I got LHS as (tan((x/2)-(pi/6))+1)^2/1-tan^2(x/2-(pi/6)) but I'm sure there must be a simple easy method to get the RHS (PS this is part of a bigger problem, I got the answer as LHS, I need to equate it to RHS for my answer to be correct

If you plot both sides you will see that the equation you wrote is not correct.

Here is a piece of advice: always try plotting first, before attempting to prove an unfamiliar result; sometimes you can save yourself hours of useless work by doing that.

 

[Krushnaraj Pandya]

If you plot both sides you will see that the equation you wrote is not correct.

Here is a piece of advice: always try plotting first, before attempting to prove an unfamiliar result; sometimes you can save yourself hours of useless work by doing that.

right, got it. I'll need to post the entire question then