RRB NTPC Mains or Stage 2 Model Paper 9 with solutions

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Question : 40 of 120

Marks: +1, -0

If

sin θ + √{sinθ + √{sinθ + √{sinθ +....∞}}}= sin^4a,

then sin θ is equal to

$sec^2 α$
$tan^2 α$
$sec^2α tan^2α$
$cos^2 α$

Solution:

(c)

sin θ + √{sin θ + √{sin θ+ √{sin θ +...∞}}}

= sec^4a = y^2

(say) ...(i)
Then, y

= √{sinθ + √{sinθ+√ {sin θ +...∞}}}

Squaring on both sides, we get

y^2 = sin θ + y

⇒ y^2 – y = sin θor y (y – 1) = sin θ

⇒ sec^2 α(sec^2 α – 1) = sinθ

[from Eq. (i),

y = sec^2α

]

⇒ sin θ = sec^2 a tan^2 α

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