NTSE Stage 2 SAT 2017 Question Paper

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Question : 58 of 100

Marks: +1, -0

If

\cos^4\θ+ \sin^2\θ= \m

, then-

$1 ≤ \m ≤ 2$
$1/2≤\m≤1$
$3/4≤\m≤1$
$3/4≤\m≤13/16$

Solution:

As given that

\sin^2\θ+\cos^2\θ=\m

⇒

\cos^4\θ+1-\cos^2=\m

Let

\cos^2\θ=\x

then relation

\cos^4\θ-\cos^2\θ+1-\m=0

become

\x^2-x+1=\m

⇒

(\x-1/2)^2+3/4=\m

as,

0≤(\x-1/2)^2≤1/4

so

3/4≤(\x-1/2)^2+3/4≤1/4+3/4

⇒

3/4≤\m≤1

So option (3) is correct.

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