$\sin (90°-\theta )\cos \theta +\cos (90°-\theta )\sin \theta =$

The given expression is: sin(90° − θ)cos(θ) + cos(90° − θ)sin(θ)    

We need to simplify the above expression step by step. First, recall the following standard trigonometric identities:

• cos 90° = 0
• sin 90° = 1

Now, applying the angle subtraction identities for sine and cosine, we have:

• sin(90° − θ) = cos(θ)
• cos(90° − θ) = sin(θ)

Thus, we can substitute these values into the original expression:

cos(θ) * cos(θ) + sin(θ) * sin(θ)    

Now, simplifying the terms:

cos²(θ) + sin²(θ)    

From the well-known Pythagorean identity in trigonometry:

cos²(θ) + sin²(θ) = 1    

Hence, the simplified value of the given expression is: 1    

In conclusion, we have successfully simplified the expression sin(90° − θ)cos(θ) + cos(90° − θ)sin(θ) to 1, using the identity cos 90° and other standard trigonometric properties.