# [HARD] Can You Help me With A Riddle of a Trig Question?

## Match each equation number with a equivalent letter, and then prove each one. (1.): (csc (x) - sin (x)) (2.): (sin (x)/(sin (x)+ cos (x)) (3.): (2 sin 4(x)) (cos 4(x)) (4.): 1+ tan(x)tan(π/2) (5.): ((sin (x)-1)/(sin (x) +1)) (A.): -(cos^2 (x)/(sin (x)+1)^2) (B.): sec (x) (C.): cos (x) cot (x) (D.): sin 8(x) (E.): tan/(1+ tan(x))

Mar 30, 2018

1 . $\left(\csc \left(x\right) - \sin \left(x\right)\right)$
$\implies \frac{1}{\sin} x - \sin x$

$\implies \frac{1 - {\sin}^{2} x}{\sin} x$

$\implies \frac{{\cos}^{2} x}{\sin} x$

$\implies \cos \left(x\right) \cot \left(x\right)$

color(white)(d

2. sin (x)/(sin (x)+ cos (x)

=>(sin x/cosx)/(sin x/cosx+ cos x/cosx

=>tan/(1+ tanx

color(white)(d

3.: $\left(2 \sin 4 x\right) \left(\cos 4 x\right)$

$\implies \sin 2 \left(4 x\right)$

$\implies \sin 8 x$

color(white)(d

5 .$\left(\frac{\sin \left(x\right) - 1}{\sin \left(x\right) + 1}\right)$

$\implies \frac{\left(\sin x - 1\right) \left(\sin x + 1\right)}{\left(\sin x + 1\right) \left(\sin x + 1\right)}$

$\implies \left(\frac{{\sin}^{2} x - 1}{\sin x + 1} ^ 2\right)$

$\implies \left(\frac{- {\cos}^{2} x}{\sin x + 1} ^ 2\right)$