SSC CGL Tier II 25 Oct 2015 Paper 1

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Question : 69 of 100

Marks: +1, -0

If

7sin^2θ + 3cos^2θ = 4

, then the value of

t a n θ

is (θ is acute)

$1/√3$
$1/√2$
$√3$
1

Solution:

(1)

7sin^2θ + 3cos^2θ = 4

On dividing both sides by

cos^2θ

,

7 {\sin ^{2} \θ}/{\cos ^{2} \θ}+ {3 \cos ^{2} \θ}/{\cos ^{2} \θ}= {4}/{\cos ^{2} \θ}

⇒ 7 \tan ^{2}\θ3=4 \sec ^{2} \θ

⇒ 7 \tan ^{2} \θ+3=4\ (1+\tan ^{2} \θ)

⇒ 7 \tan ^{2} \θ+3=4+4 \tan ^{2} \θ

⇒ 7 \tan ^{2} \θ-4 \tan ^{2} \θ=4-3

⇒ 3 \tan ^{2} \θ=1 ⇒ \tan ^{2} \θ= {1}/{3}

⇒ \tan \θ= {1}/{√{3}}

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