Inverse Trigonometric FunctionHard
Question
The value of tan-1
+ tan-1
+ tan-1 
, where a, b, c ∈ R+ and λ = a + b + c, is equal to-
+ tan-1 + tan-1 , where a, b, c ∈ R+ and λ = a + b + c, is equal to-Options
A.π/4
B.π
C.π/2
D.None
Solution
tan-1a 
+ tan-1b 
+ tan-1c 
Now
tan-1a
+ tan-1b 
+ tan-1c 
Put
= y
tan-1ay + tan-1by + tan-1cy
= π - tan-1
= tan-1y
Now a + b + c = abcy2 = π
+ tan-1b + tan-1c Now
tan-1a
+ tan-1b + tan-1c Put
= ytan-1ay + tan-1by + tan-1cy
= π - tan-1
= tan-1y
Now a + b + c = abcy2 = π
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