Question

If the angles are represented in degrees, find both angles: sin(x+7)=cos(4x+8)

Answer 1

`m\angle 1 = 22\degree`

`m\angle 2 = 68\degree`

Explanation:

`\sin(x + 7) = \cos(4x + 8) \\ \sin(x + 7) = \sin \{90 - (4x + 8) \} \\ \{ \because \cos \theta = \sin(90 \degree - \theta) \}\\ \therefore \: (x + 7) = 90 - (4x + 8) \\ x + 7 + 4x + 8 = 90 \\ 5x = 90 - 15 \\ 5x = 75 \\ x = (75)/(5) \\ x = 15`

(x + 7)° = (15 + 7)° = 22°

(4x + 8)° = (4*15 + 8)° = (60 + 8)° = 68°

`m\angle 1 = 22\degree`

`m\angle 2 = 68\degree`