1. ## Hard Trig Proof

$\displaystyle tanxsinx + cosx = \frac{1}{cosx}$

$\displaystyle RS = \frac{1}{cosx}$

$\displaystyle = \frac{tanx}{sinx}$

$\displaystyle = \frac{sinx}{sinxcosx}$

$\displaystyle = \frac{sinxtanx}{sinxcosxtanx}$

$\displaystyle = \frac{sinxtanx}{sinxsinx}$

$\displaystyle = \frac{sinxtanx}{sin^2x}$

$\displaystyle = \frac{sinxtanx}{1 - cos^2x}$

What do I do from here? Is there a simpler way of solving this?

2. $\displaystyle \tan{x}\sin{x}+\cos{x} =$

$\displaystyle \frac{\sin{x}}{\cos{x}} \cdot \sin{x} + \cos{x} \cdot \frac{\cos{x}}{\cos{x}} =$

$\displaystyle \frac{\sin^2{x}}{\cos{x}} + \frac{\cos^2{x}}{\cos{x}} =$

put them together and finish.

3. just to mention about solving identities this one being an example

try to get everything into sin and cos. then the identities are easy to see.

keepimg tan in this one made things more difficult.

4. tan x sin x + cos x = 1/cos x

tan x ( tan x cos x) + cos x =

tan^2 x cos x + cos x =

cos x (tan^2 x + 1) =

cos x(sec^2 x) =

cos x (1/cos x)(1/cos x) = ?

voila!