Question

(1+sint)(1+cost)=5/4 then (1-sint)(1-cost)

Answer 1

Answer:

(1-sint)(1-cost) = 13/4  - √10

Step-by-step explanation:

Given

(1+sint)(1+cost)=5/4

=> 1  + sint + cost + sintCost  = 5/4

=> 2 + 2Sint + 2Cost + 2SintCost = 5/2

=> 1 + 1 + 2Sint + 2Cost + 2SintCost = 5/2

=> Sin²t + Cos²t  + 2SintCost  + 2(Sint + Cost)  - 3/2  = 0

=> (Sint + Cost)² + 2(Sint + Cost) - 3/2 = 0

Let say Sint + Cost = X

=> X² + 2X - 3/2 = 0

=> X = (- 2 ± √(4 + 6))/2

=> X = - 1 ± √10 / 2

only Possible Solution

X = √10 / 2  -  1

=> Sint + Cost = √10 / 2  -  1

1  + sint + cost + sintCost  = 5/4

=> sintCost = 1/4 - (sint + cost)

to find :

(1-sint)(1-cost)

= 1 - (sint + cost) + sintCost

= 1 - (sint + cost) +  1/4 - (sint + cost)

= 5/4 - 2(sint + cost)

= 5/4 - 2(√10 / 2  -  1)

= 5/4 - √10 + 2

= 13/4 - √10

(1-sint)(1-cost) = 13/4  - √10