RRB NTPC Mains or Stage 2 Model Paper 4 with solutions

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Question : 40 of 120

Marks: +1, -0

If

{tanθ+ cot θ}/{tanθ- cot θ}=2,

(0 < θ < 90° ), then the value of sin θ is

$2 /√3$
$√ 3/ 2$
$1 /2$
1

Solution:

(b)

{tan θ+cotθ }/{tanθ- cot θ}=2/1

By componendo and dividendo,

{2tanθ}/{2cotθ}= 3/ 1

⇒

{sinθ}/{cosθ} . {sinθ} /{ cosθ}=3

⇒ sin^2 q = 3 cos^2θ

⇒sin^2 θ = 3 (1 – sin^2 θ)

⇒ 4 sin^2 θ= 3

⇒ sin^2 θ =3/4

⇒ sinθ =√3/2

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