Question

Sin65°cos25 °+sin25 °cos65 °​

Answer 1

`sin(65\º)cos(25\º) + sin(25\º)cos(65\º) = sin(65\º + 25\º) = sin(90\º) = \sin{(\pi)/(2)} = 1`

Explanation:

We use trigonometric identities to solve this question:

`sin(A + B) = sin(A)cos(B) + sin(B)cos(A)`

In this problem:

We have the right side of the equality, that is:

`sin(65\º)cos(25\º) + sin(25\º)cos(65\º) = sin(A)cos(B) + sin(B)cos(A)`

Which means that
`A = 65\º, B = 25\º`

Then

`sin(65\º)cos(25\º) + sin(25\º)cos(65\º) = sin(65\º + 25\º) = sin(90\º) = \sin{(\pi)/(2)} = 1`