SSC CPO SI and ASI 2015 Paper

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Question : 148 of 199

Marks: +1, -0

If sin

^{4}

θ + cos

^{4}

θ = 2 sin

^{2}

θ cos

^{2}

θ (θ is an acute angle), then the value of tan θ is

1
2
$\ √{2}$
0

Solution:

(1)

\sin ^{4} \ θ+\cos ^{4} \ θ-2 \sin ^{2} \θ \cos ^{2} \θ=0

(\sin ^{2} \θ-\cos ^{2} \θ\ )^{2}=0

\⇒ \sin ^{2} \θ=\cos ^{2} \θ

\tan ^{2} θ=1 \⇒ \tan \θ=1

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