if (1+cost)(1+sint)=5/4 then find value of

(1-cost)(1-sint) .

Given the equation:

(1 + cos t)(1 + sin t) = 5/4

We need to determine the value of (1 - cos t)(1 - sin t).

Step 1: Expand the Given Expression
Expanding the left-hand side:

(1 + cos t)(1 + sin t) = 1 + sin t + cos t + sin t cos t

So, we rewrite the equation as:

1 + sin t + cos t + sin t cos t = 5/4

Step 2: Find the Value of (1 - cos t)(1 - sin t)
Expanding the required expression:

(1 - cos t)(1 - sin t) = 1 - sin t - cos t + sin t cos t

Now, using the given equation:

1 + sin t + cos t + sin t cos t = 5/4

Rearrange to isolate (sin t + cos t + sin t cos t):

sin t + cos t + sin t cos t = 5/4 - 1
sin t + cos t + sin t cos t = 1/4

Now, subtract this from 1:

(1 - cos t)(1 - sin t) = 1 - (sin t + cos t + sin t cos t)
= 1 - 1/4
= 3/4

Final Answer:
(1 - cos t)(1 - sin t) = 3/4