If sin A + sin B + sin C + sin D = 4, then find sin A . sin B . sin C . sin D

We shall use the range of sine function to solve this problem

Answer: If sin A + sin B + sin C + sin D = 4, the value of sin A . sin B . sin C . sin D is 1.

Let us solve the problem.

Explanation:

The range of sin function is [-1, 1].

Therefore, the maximum value that the sine function can attain is 1.

Since sin A + sin B + sin C + sin D = 4, sin A = sin B = sin C = sin D = 1.

Thus, the value of sin A . sin B . sin C . sin D = 1⁴ = 1.

Therefore, the value of sin A . sin B . sin C . sin D = 1.