If x=5,y=6,z=7.The value of `sin^(2)((X+Y)/2)`, is

Options

A. `3/5`
B. `4/5`
C. `2/5`
D. `1/5`

Explanation

To find the value of \( \sin^2\left(\frac{x+y}{2}\right) \) given \( x = 5 \), \( y = 6 \), and \( z = 7 \), we can follow these steps:

### Step 1: Use the triangle angle sum property
In any triangle, the sum of the angles is \( \pi \) (or 180 degrees). Therefore, we have:
\[ x + y + z = \pi \]
From this, we can express \( x + y \) in terms of \( z \):
...