Express sin 75° + cos 65° in terms of trigonometric ratios of angles between 0^o and 45^o.

Given: sin 75° + cos 65°.

We can write,

75° = 90° - 15°

& 65° = 90° - 25°

Then, sin 75° + cos 65° = sin (90° - 15°) + cos (90° - 25°)

⇒ sin 75° + cos 65° = cos 15° + sin 25°

[∵, sin (90° - θ ) = cos θ & cos (90° - θ) = sin θ]

In cos 15° + sin 25°, 15° & 25° both are angles between 0° and 45°.

Thus, answer is sin 75° + cos 65° = cos 15° + sin 25°.