NIMCET 2020 Question Paper with solutions

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Question : 39 of 120

Marks: +1, -0

If

{\tan x}/2={\tan y}/3={\tan z}/5

and

x+y+z=π

,then the value of

\tan^2x+\tan^2y+\tan^2z

is

38/3
38
114
None of these

Solution:

x+y+z=π

Let

{\tan x}/2={\tan y}/3={\tan z}/5=1

∴\tan x+\tan y+\tan z=\tan x\;\tan y\;\tan z

∴2λ+3λ+5λ=(2λ)(3λ)(5λ)

10λ=30λ^3

λ^2=1/3

Now,

\tan^2 x+\tan^2 y+\tan^2 z

4λ^3+9λ^2+25λ^2

⇒38λ^2=38×1/3

=38/3

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