Trigonometric Identities
Problems
Problem : Prove the following identity: tan(θ)cos(θ) = sin(θ)
Problem : Prove the following identity: (sin(θ))4 +2(sin(θ))2(cos(θ))2 + (cos(θ))4 = tan(θ)cot(θ)
| (sin(θ))4 +2(sin(θ))2(cos(θ))2 + (cos(θ))4 = tan(θ)cot(θ) |
(sin(θ))4 +2(sin(θ))2(cos(θ))2 + (cos(θ))4 =
|
| (sin(θ))4 +2(sin(θ))2(cos(θ))2 + (cos(θ))4 = 1 |
| ((sin(θ))2 + (cos(θ))2)((sin(θ))2 + (cos(θ))2) = 1 |
| (1)(1) = 1 |
Problem :
Prove the following identity:
- cos(θ)(cot(θ))2 = cot(θ)sin(θ)
- cos(θ)(cot(θ))2 = cot(θ)sin(θ)
|
- =
|
- = cos(θ)
|
- = 1
|
| (csc(θ))2 - (cot(θ))2 = 1 |
| (csc(θ))2 = 1 + (cot(θ))2 |
= sin(θ)
- cos(θ)(cot(θ))2 = cot(θ)sin(θ)
=
-
= 1




