Question

class 11 maths question

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

then find the value 0f (1-sint)(1-cost)


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Answer 1

Answer:

The answer is

(1-sint)(1-cost) = 13/4  - √10

Step-by-step explanation:

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

On multiplication

=> 1  + sint + cost + sintCost  = 5/4

Multiplying both sides by 2 we get

=> 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 x = Sint + Cost

Which leads to

=> X² + 2X - 3/2 = 0

Which is a quadratic equation in x

So

X = (- 2 ± √(4 + 6))/2

=> X = - 1 ± √10 / 2

Now X = - 1 - √10 / 2 is impossible

So

X = √10 / 2  -  1

=> Sint + Cost = √10 / 2  -  1

Again by the given condition

1  + sint + cost + sintCost  = 5/4

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

So

(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

Hence

(1-sint)(1-cost) = 13/4  - √10

Answer 2

Answer:

Use the trig identity: # tan (a + b) = (tan a + tan b)/(1 - tan a.tan b)#

#(tan 80 + tan 55)/(1 - tan 80.tan 55) = tan (80 + 55) = tan 135^@#