If `tanalpha` is equal to the integral solution of the inequality `4x^2-16 x+15<0` and `cosbeta` is equal to the slope of the bisector of the first quadrant, then `sin(alpha+beta)sin(alpha-beta)` is equal to (a)`3/5` (b) `3/5` (c) `2/(sqrt(5))` (d) `4/5`

Explanation

To solve the problem step by step, we will follow the instructions given in the video transcript.

### Step 1: Solve the Inequality
We start with the inequality:
\[ 4x^2 - 16x + 15 < 0 \]

First, we need to find the roots of the corresponding quadratic equation:
\[ 4x^2 - 16x + 15 = 0 \]
...