Question

In a right angled triangle acute angle α, β satisfy tan

α + tan β + tan²α + tan²β = 4, if hypotenuse is of length d then area of ∆ is-

• A. $\frac { \sqrt { 3 } } { 4 }$ d²
• B.
• C. $\frac { \mathrm { d } ^ { 2 } } { 4 }$
• D. $\frac { \sqrt { 3 } } { 8 }$ d²

Answer 1

Answer: (C)

$\frac { \mathrm { d } ^ { 2 } } { 4 }$

Answer 2

Q α + β = 90⁰

∴ tan α + cot α + tan² β + cot² β = 4

Let tan α = t

∴ t + $\frac { 1 } { \mathrm { t } }$ + t² + = 4

∴ t = 1 satisfy

α = β = 45⁰

So area is $\frac { \mathrm { d } ^ { 2 } } { 4 }$