If α +β =(π /4), then the value of (1+ tan α ) (1+ tan β ) is equal to

Question

If α +β =(π /4), then the value of (1+ tan α ) (1+ tan β ) is equal to (A)  1  (B)  -1  (C)  2  (D)  -2

Tardigrade Admin · Accepted Answer

Given, α +β =(π /4) ∴ tan (α +β )= tan ( (π /4) )=1 ⇒ tan α + tan β =1- tan α tan β ⇒ tan α + tan β + tan α tan β =1 ..(i) Now, (1+ tan α ) (1+ tan β ) =1+ tan α + tan β + tan α tan β =1+1=2 [using Eq. (i)]

Q. If $α + β = \frac{π}{4},$ then the value of $(1 + tan α)$ $(1 + tan β)$ is equal to

$1$

$- 1$

$2$

$- 2$

Given, $α + β = \frac{π}{4}$
$∴$ $tan (α + β) = tan (\frac{π}{4}) = 1$
$\Rightarrow$ $tan α + tan β = 1 - tan α t an β$
$\Rightarrow$ $tan α + tan β + tan α tan β = 1$ ..(i)
Now, $(1 + tan α) (1 + tan β)$
$= 1 + tan α + tan β + tan α tan β$
$= 1 + 1 = 2$ [using Eq. (i)]

Q. If α+β=4π​, then the value of (1+tanα) (1+tanβ) is equal to

1

−1

2

−2

Given, α+β=4π​ ∴ tan(α+β)=tan(4π​)=1 ⇒ tanα+tanβ=1−tanαtanβ ⇒ tanα+tanβ+tanαtanβ=1 ..(i) Now, (1+tanα)(1+tanβ) =1+tanα+tanβ+tanαtanβ =1+1=2 [using Eq. (i)]

Q. If $α + β = \frac{π}{4},$ then the value of $(1 + tan α)$ $(1 + tan β)$ is equal to

$1$

$- 1$

$2$

$- 2$

Given, $α + β = \frac{π}{4}$
$∴$ $tan (α + β) = tan (\frac{π}{4}) = 1$
$\Rightarrow$ $tan α + tan β = 1 - tan α t an β$
$\Rightarrow$ $tan α + tan β + tan α tan β = 1$ ..(i)
Now, $(1 + tan α) (1 + tan β)$
$= 1 + tan α + tan β + tan α tan β$
$= 1 + 1 = 2$ [using Eq. (i)]