Identidades trigonométricas Ayúdenme a resolver los ejercicios por favor?

Hola.

1. <img src="https://tex.z-dn.net/?f=2%281-cos%5E%7B2%7D%20%20%5Calpha%20%29%2Bcos%5E%7B2%7D%20%20%5Calpha%3D%201%2Bsen%5E%7B2%7D%20%20%5Calpha%20" />

Usando las identidades <img src="https://tex.z-dn.net/?f=sen%5E%7B2%7D%20%20%5Calpha%20%3D1-cos%5E%7B2%7D%20%20%5Calpha%20" /> <img src="https://tex.z-dn.net/?f=cos%5E%7B2%7D%20%5Calpha%20%3D%201-sen%5E%7B2%7D%20%20%20%5Calpha%20" />

<img src="https://tex.z-dn.net/?f=2%28sen%5E%7B2%7D%20%20%5Calpha%20%29%2B%281-sen%5E%7B2%7D%20%20%5Calpha%20%29%3D1%2Bsen%5E%7B2%7D%20%5Calpha" />

<img src="https://tex.z-dn.net/?f=1%2B2sen%5E%7B2%7D%20%20%5Calpha%20-sen%5E%7B2%7D%20%20%5Calpha%20%3D%201%2Bsen%5E%7B2%7D%20%20%5Calpha%20" />

<img src="https://tex.z-dn.net/?f=1%2Bsen%5E%7B2%7D%20%20%5Calpha%20%3D%201%2Bsen%5E%7B2%7D%20%20%5Calpha%20%20%20" /> <img src="https://tex.z-dn.net/?f=%2F%2FDemostrado." />

2.

<img src="https://tex.z-dn.net/?f=%281%2Bsen%28%20%5Calpha%29%29%281-sen%28%20%5Calpha%20%29%29%3Dcos%5E%7B2%7D%20%20%20%5Calpha%20" />

Usando el producto notable "suma por diferencia"

<img src="https://tex.z-dn.net/?f=%28a%2Bb%29%28a-b%29%20%3D%20a%5E%7B2%7D%20-b%5E%7B2%7D%20" />

Tenemos

<img src="https://tex.z-dn.net/?f=%20%281%2Bsen%28%20%5Calpha%29%29%281-sen%28%20%5Calpha%20%29%29%3Dcos%5E%7B2%7D%20%20%20%5Calpha%20" />

[img = 10] / / Identidad del ejercicio 1

[img = 11] [img = 12]

3.

[img = 13]

Usando la identidad [img = 14]

[img = 15]

[img = 16]

[img = 17]

Simplificamos cos(α)

[img = 18] [img = 19]

Un cordial saludo.