Write the value of sin A cos (90° − A) + cos A sin (90° − A).

To find: sin A cos (90° − A) + cos A sin (90° − A)

∵ cos (90° – A) = sin A and sin (90° – A) = cos A ……………(i)

∴ sin A cos (90° − A) + cos A sin (90° − A)

= sin A sin A + cos A cos A [Using (i)]

= sin² A + cos² A

Now, ∵ sin² θ + cos² θ = 1

∴ sin A cos (90° − A) + cos A sin (90° − A)

= sin² A + cos² A = 1