Question

tanalpha, tanbeta, tangamma are the roots of the equation x^3 -px^2 -r = 0 then find the value of (1 + tan^2 alpha)(1 + tan^2 beta)(1 + tan^2 gamma).

Options given:
a) 1 + (p - r)^2
b) 2 + (p - r)^2
c) 3 + (p + r)^2
d) 1 - (p - r)^2


I give away 30 points, but please give me the right answer
thanks in advance

Answer 1

Answer:

★᭄ꦿ᭄Answer★᭄ꦿ᭄

Correct option is

D

Given:

⇒tan(θ+ 4π )=3tan3θ

⇒ 1−tan 0/21+tan 0/2 =3

1−3tan 2 θ3tanθ−tan 3 θ

⇒tan (4) θ−2tan (2)θ+ 8/3 tanθ− 1/3

=0

⇒tan (4) θ+0tan

3 θ−2tan 2 θ+

8/3 tanθ− 1/3 =0

Therefore sum of roots is,

tanα+tanβ+tanγ+tanδ=0

Step-by-step explanation:

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