Question

Identidades trigonometricas

Answer 1

SOLUCIÓN :

1) Cos x * secx = 1

Cos x * 1/ cos x = 1

1 = 1

2) Senx * Cscx = 1

Senx * 1/ senx = 1

1 = 1

3) ( 1 + cosx ) * ( 1 - cosx)= sen²x

1 - cos²x = sen²x

sen²x = sen²x

4) Senx /( 1 - Cosx )= Csc x

Senx/( 1- Cosx)* ( 1+Cosx)/ (1 + Cosx) = Cscx

Senx * ( 1 + Cosx ) / ( 1 - Cos²x ) = Csc x

Senx * ( 1+ cosx)/ sen²x = Cscx

( 1 + Cosx ) / Senx = 1 / senx

5) ( cosx / senx ) + sen x = Csc x

(cos x+ sen²x ) / senx = 1 / senx

6) Tan²x * Cos²x = 1 - cos²x

Sen²x/cos²x * cos²x = 1- cos²x

Sen²x = 1 - cos²x

Sen²x = sen²x

7) Csc x /(Ctgx + tanx )= cosx

1/senx / ( Cosx/senx + senx /cosx ) = cosx

1/ senx / ( Cos²x + Sen²x)/Senx*cosx = cosx

1 / senx / 1 / senx * cosx = cosx

Senx * cosx / senx = cosx

cosx = cosx

8) Secx + Tanx = cosx /( 1 - senx )

1 / cosx + Senx / cosx = cosx /( 1 - senx )* ( 1+ senx )/ ( 1+ senx )

( 1 + senx) / cosx = cosx*( 1+ senx) / ( 1-sen²x)

( 1+ senx )/ cosx = cosx* ( 1+ senx )/ cos²x

( 1 + sen x)/ cosx = ( 1+ senx )/ cosx

9) ( 1 + senx )/senx = 1+ cscx

( 1+ senx )/ senx = ( 1+ 1/senx )

( 1+ senx )/ senx = ( senx +1 )/ senx

10 ) ( sen²x - tan²x) / cscx = senx

( sen²x - sen²x/ cos²x )/ 1 / senx= senx

( sen²x* cos²x- sen²x)/ cos²x / 1 / sen x = sen x

sen²x* ( cos²x- 1)/ cos²x /1/senx = senx

- sen⁵x /cos²x = senx

11) senx /( cosx +1) + cosx / secx =1

senx/ ( cosx +1 ) + cosx / 1 / cosx = 1

senx / ( cosx +1) + cos²x = 1

senx / ( cosx +1 ) * ( cosx -1)/ ( cosx-1 ) + cos²x = 1

senx * ( cosx -1 ) /( cos²x -1) + cos²x = 1

senx * ( cosx - 1)/- sen²x+ cos²x = 1

( 1- cosx) / senx + cos²x = 1

12 ) cosx / csc x + cosx / ( secx -1 ) = 2 * tanx

cosx / 1 /senx + cosx /( 1/ cosx -1 ) = 2* tanx

senx * cosx + cos²x/ ( 1- cosx ) = 2 * senx / cosx

13) ( 1-cosx )/( 1 +cosx ) = ( secx -1)/( secx +1)

( 1-cosx )/( 1+cosx )= ( 1 / cosx -1 )/( 1 / cosx +1 )

( 1 - cosx ) / ( 1+cosx ) = ( 1-cosx)/cosx /( 1+cosx )/cosx

( 1 - cosx )/ ( 1+cosx ) = ( 1-cosx ) / ( 1+cosx )

14) 1 / cosc²x + 1 / sec²x = 1

1/1/sen²x + 1 / 1 / cos²x = 1

sen² x + cos²x = 1

1 = 1

15 ) cotgx + senx / ( 1+ cosx ) = coscx

cosx / senx + senx / ( 1+cosx ) = 1/senx

cosx * ( 1 + cosx ) + sen²x / senx * ( 1 + cosx ) = 1 / sen x

( cosx + cos²x + sen²x ) / senx * ( 1 + cosx ) = 1 / senx

( cosx + 1 )/ senx * ( 1+ cosx ) = 1 / senx

1 / senx = 1 / senx

coscx = coscx

Answer 2

Respuesta:

1) Cos x * secx = 1

Cos x * 1/ cos x = 1

1 = 1

2) Senx * Cscx = 1

Senx * 1/ senx = 1

1 = 1

3) ( 1 + cosx ) * ( 1 - cosx)= sen²x

1 - cos²x = sen²x

sen²x = sen²x

4) Senx /( 1 - Cosx )= Csc x

Senx/( 1- Cosx)* ( 1+Cosx)/ (1 + Cosx) = Cscx

Senx * ( 1 + Cosx ) / ( 1 - Cos²x ) = Csc x

Senx * ( 1+ cosx)/ sen²x = Cscx

( 1 + Cosx ) / Senx = 1 / senx

5) ( cosx / senx ) + sen x = Csc x

(cos x+ sen²x ) / senx = 1 / senx

6) Tan²x * Cos²x = 1 - cos²x

Sen²x/cos²x * cos²x = 1- cos²x

Sen²x = 1 - cos²x

Sen²x = sen²x

7) Csc x /(Ctgx + tanx )= cosx

1/senx / ( Cosx/senx + senx /cosx ) = cosx

1/ senx / ( Cos²x + Sen²x)/Senx*cosx = cosx

1 / senx / 1 / senx * cosx = cosx

Senx * cosx / senx = cosx

cosx = cosx

8) Secx + Tanx = cosx /( 1 - senx )

1 / cosx + Senx / cosx = cosx /( 1 - senx )* ( 1+ senx )/ ( 1+ senx )

( 1 + senx) / cosx = cosx*( 1+ senx) / ( 1-sen²x)

( 1+ senx )/ cosx = cosx* ( 1+ senx )/ cos²x

( 1 + sen x)/ cosx = ( 1+ senx )/ cosx

9) ( 1 + senx )/senx = 1+ cscx

( 1+ senx )/ senx = ( 1+ 1/senx )

( 1+ senx )/ senx = ( senx +1 )/ senx

10 ) ( sen²x - tan²x) / cscx = senx

( sen²x - sen²x/ cos²x )/ 1 / senx= senx

( sen²x* cos²x- sen²x)/ cos²x / 1 / sen x = sen x

sen²x* ( cos²x- 1)/ cos²x /1/senx = senx

- sen⁵x /cos²x = senx

11) senx /( cosx +1) + cosx / secx =1

senx/ ( cosx +1 ) + cosx / 1 / cosx = 1

senx / ( cosx +1) + cos²x = 1

senx / ( cosx +1 ) * ( cosx -1)/ ( cosx-1 ) + cos²x = 1

senx * ( cosx -1 ) /( cos²x -1) + cos²x = 1

senx * ( cosx - 1)/- sen²x+ cos²x = 1

( 1- cosx) / senx + cos²x = 1

12 ) cosx / csc x + cosx / ( secx -1 ) = 2 * tanx

cosx / 1 /senx + cosx /( 1/ cosx -1 ) = 2* tanx

senx * cosx + cos²x/ ( 1- cosx ) = 2 * senx / cosx

13) ( 1-cosx )/( 1 +cosx ) = ( secx -1)/( secx +1)

( 1-cosx )/( 1+cosx )= ( 1 / cosx -1 )/( 1 / cosx +1 )

( 1 - cosx ) / ( 1+cosx ) = ( 1-cosx)/cosx /( 1+cosx )/cosx

( 1 - cosx )/ ( 1+cosx ) = ( 1-cosx ) / ( 1+cosx )

14) 1 / cosc²x + 1 / sec²x = 1

1/1/sen²x + 1 / 1 / cos²x = 1

sen² x + cos²x = 1

1 = 1

15 ) cotgx + senx / ( 1+ cosx ) = coscx

cosx / senx + senx / ( 1+cosx ) = 1/senx

cosx * ( 1 + cosx ) + sen²x / senx * ( 1 + cosx ) = 1 / sen x

( cosx + cos²x + sen²x ) / senx * ( 1 + cosx ) = 1 / senx

( cosx + 1 )/ senx * ( 1+ cosx ) = 1 / senx

1 / senx = 1 / senx

coscx = coscx