Answer:
[tex]\sin{65\º}\cos{25\º} + \sin{25\º}\cos{65\º} = \sin{65\º + 25\º} = \sin{90\º} = \sin{\frac{\pi}{2}} = 1[/tex]
Step-by-step explanation:
We use trigonometric identities to solve this question:
[tex]\sin{A + B} = \sin{A}\cos{B} + \sin{B}\cos{A}[/tex]
In this problem:
We have the right side of the equality, that is:
[tex]\sin{65\º}\cos{25\º} + \sin{25\º}\cos{65\º} = \sin{A}\cos{B} + \sin{B}\cos{A}[/tex]
Which means that [tex]A = 65\º, B = 25\º[/tex]
Then
[tex]\sin{65\º}\cos{25\º} + \sin{25\º}\cos{65\º} = \sin{65\º + 25\º} = \sin{90\º} = \sin{\frac{\pi}{2}} = 1[/tex]
