Evaluate Trigonometric Expression

The question asks for the value of the expression $\sin^2 90^\circ + \cos^2 60^\circ$. We need to find the values of $\sin 90^\circ$ and $\cos 60^\circ$ and substitute them into the expression.

Step 1: Find Standard Trigonometric Values

• The value of $\sin 90^\circ$ is 1.
• The value of $\cos 60^\circ$ is $\frac{1}{2}$.

Step 2: Substitute Values into the Expression

Substitute the known values into the given expression:

$ \sin^2 90^\circ + \cos^2 60^\circ = (\sin 90^\circ)^2 + (\cos 60^\circ)^2 $

$ = (1)^2 + \left(\frac{1}{2}\right)^2 $

Step 3: Calculate the Result

Perform the squaring and addition:

$ = 1 + \frac{1}{4} $

To add these, find a common denominator:

$ = \frac{4}{4} + \frac{1}{4} $

$ = \frac{4 + 1}{4} $

$ = \frac{5}{4} $

Conclusion

The value of the expression $\sin^2 90^\circ + \cos^2 60^\circ$ is $\frac{5}{4}$. This matches Option A.