This document contains 10 trigonometric identity problems worked out step-by-step. Each problem presents an identity, the solution steps showing the manipulations using trigonometric definitions and rules, and a statement verifying that the resulting expression is an identity. Some examples verified include cscθcosθ = cotθ, cscθtanθ = secθ, and (secθ - 1)(secθ + 1) = tan2θ.

1. D É C I M O G R A D O
Solución Taller Identidades

2. 1. cscθcos θ = cot θ, Solución:



 sensen
cos
cos
1





sensen
coscos

V E R I F I C A M O S Q U E S I
E S U N A I D E N T I D A D

3. 2. Cscθ tan θ = sec θ, Solución:


 cos
1
cos
1

sen
sen
 cos
1
cos
1

V E R I F I C A M O S Q U E S I
E S U N A I D E N T I D A D

4. 5. cosθ(tan θ+cot θ) = csc θ,
Solución:





sensen
sen 1
)
cos
cos
(cos 
 sensen
11




sensen
sen 1
)
cos
cos
(cos
22


bn
bman
n
m
b
a 
Recordemos
Entonces:
1cos22
 senRecordar
1
V E R I F I C A M O S Q U E S I
E S U N A I D E N T I D A D

5. 6. senθ(cot θ+tan θ) = sec θ,
Solución:





cos
1
)
cos
cos
( 
sen
sen
sen
 cos
1
cos
1




cos
1
)
cos
cos
(
22


sen
sen
sen
V E R I F I C A M O S Q U E S I
E S U N A I D E N T I D A D

6. 7. tanθ cot θ - cos2 θ = Sen2 θ,
Solución:




 22
cos
cos
cos
sen
sen
sen

 22
cos1 sen
 22
cos1cos1 
V E R I F I C A M O S Q U E S I
E S U N A I D E N T I D A D

7. 8. senθ csc θ - cos2 θ = Sen2 θ,
Solución:


 22
cos
1
sen
sen
sen 
 22
cos1 sen
 22
cos1cos1 
V E R I F I C A M O S Q U E S I
E S U N A I D E N T I D A D

8. 9. (sec θ- 1)(sec θ + 1) = tan2 θ,
Solución:
Recordar:
 222
tan1sec 
22
))(( bababa 
1sec1sec 22
 
 2
tan)1)(sec1(sec 
V E R I F I C A M O S Q U E S I
E S U N A I D E N T I D A D
 22
tantan 

9. 10. (csc θ- 1)(csc θ + 1) = cot2 θ,
Solución:
Recordar:
 222
cot1csc 
22
))(( bababa 
1csc1csc 22
 
V E R I F I C A M O S Q U E S I
E S U N A I D E N T I D A D