Question

AYUDA Demostrar las siguientes identidades trigonométricas

1. sen x ctg x = cos x
2. cos x tg x = sen x

3. ctg x sec x = cosec x

4. sen x sec x = tg x

5. cos x cosec x = ctg x

6 ctg x sec x sen x = 1

7 (1 - cos² x) cosec² x = 1

8 (1 - sen² x) sec² x = 1

9 ctg² x (1 - cos² x) = cos² x

10 (1 - cos² x) sec² x = tg² x

Answer 1

sen x ctg x = cos x
$senx( \frac{cosx}{snx} ) = cosx$
cosx = cosx


cos x tg x = sen x
$cosx( \frac{senx}{cosx} ) = senx$
senx = senx


ctg x sec x = cosec x
$( \frac{cosx}{senx} )( \frac{1}{cosx})$ = cscx
$\frac{1}{senx} = cscx$
cscx = cscx



sen x sec x = tg x
$senx( \frac{1}{cosx}) = tgx$
tgx = tgx


cos x cosec x = ctg x
$cosx( \frac{1}{senx}) = ctgx$
$\frac{cosx}{senx} = ctgx$



ctg x sec x sen x = 1
$( \frac{cosx}{senx} )( \frac{1}{cosx})(senx) = 1$
1 = 1


 (1 - cos² x) cosec² x = 1
$sen ^{2}x( \frac{1}{ sen^{2} x } ) = 1$
1 = 1


(1 - sen² x) sec² x = 1
$( cos^{2}x)( \frac{1}{cos^{2} x} ) = 1$
1 = 1


ctg² x (1 - cos² x) = cos² x
$( \frac{cos^{2}x }{sen^{2}x } )( sen ^{2}x ) = cos^{2}x$
$cos^{2}x = cos^{2}x$


(1 - cos² x) sec² x = tg² x
$sen^{2}x( \frac{1}{cos^{2}x}) = tg^{2}x$
$tg^{2}x = tg^{2} x$

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