Originally Posted by

**KarlosK** The first question I think I have the correct answer to but wanted to double check.

The problem says prove the following identity...

sec x + csc x = csc x + csc x tan x

(1/cosx + 1/sin)=

sinx/(sinxcosx) + cosx/(sinxcosx)

(1/sinx)*(sinxcosx)= cscxtanx=secx

Does this answer make sense? no

working from the right side ...

$\displaystyle \textcolor{red}{\csc{x} + \csc{x}\tan{x}}$

$\displaystyle \textcolor{red}{\csc{x} + \frac{1}{\sin{x}} \cdot \frac{\sin{x}}{\cos{x}}}$

$\displaystyle \textcolor{red}{\csc{x} + \frac{1}{\cos{x}}}$

$\displaystyle \textcolor{red}{\csc{x} + \sec{x}}$

The second question I have I need to reduce this to a single term.

tan (x+y) - tan y

-----------------------

1+ tan (x+y) tan y

use this identity ...

$\displaystyle \textcolor{red}{\tan(a-b) = \frac{\tan{a}-\tan{b}}{1+\tan{a}\tan{b}}}$

let $\displaystyle \textcolor{red}{a = (x+y)}$ and $\displaystyle \textcolor{red}{b = y}$