Question

Demostrar las siguientes identidades trigonométricas (proceso, en fotos si puede):
1. (Cosx/coscx) + (cosx/sec-1) = 2tanx
2. (Sen^2x-tan^2x)/coscx= Senx
3. Senx/1-cosx =cscx
4. Tanx+cotx=secx*cscx
5. sen^2x+sen^2x*tan^2x= tan^2x
6. 1/cosec^2x + 1/sec^2x= 1

Answer 1

El primero me parece que hay un error, 
el segundo también...

Para el tercero:

$\frac{sin(x)}{1-cos(x)} =csc(x)$

$\frac{sin(x)}{1-cos(x)}( \frac{1+cos(x)}{1+cos(x)} )= \frac{sin(x)(1+cos(x))}{1-cos ^{2}(x) } = \frac{sin(x)(1+cos(x))}{sin ^{2}(x) } = \frac{1+cos(x)}{sin(x)} =... \\ \\ ...= \frac{1}{sin(x)} + \frac{cos(x)}{sin(x)} =csc(x)+ctg(x)$

cuarta:

$tan(x)+ctg(x)=sec(x)csc(x) \\ \\ \frac{sin(x)}{cos(x)} + \frac{cos(x)}{sin(x)} \\ \\ \frac{sin^{2}(x)+cos ^{2}(x) }{sin(x)cos(x)} \\ \\ \frac{1}{sin(x)cos(x)} = (\frac{1}{sin(x)} )( \frac{1}{cos(x)} )=csc(x)sec(x)$

quinta:

$sin^{2} (x)+(sin^{2} (x))tan ^{2} (x)=tan ^{2} (x) \\ \\ sin^{2} (x)(1+tan^{2}(x) ) \\ sin^{2} (x)(sec ^{2}(x) ) \\ sin ^{2} (x)( \frac{1}{cos ^{2}(x) } ) \\ \frac{sin^{2}(x) }{cos^{2}(x) } =tan ^{2} (x)$

sexta:

$\frac{1}{csc ^{2}(x) } + \frac{1}{sec^{2}(x) } =1 \\ \\ \frac{1}{ \frac{1}{sen^{2}(x) } } +\frac{1}{ \frac{1}{cos^{2}(x) } } = sin ^{2} (x)+ cos^{2}(x) =1$