Haryana Police Constable Model Paper 1

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Question : 24 of 100

Marks: +1, -0

The value of

\tan70°\tan20° + \sin^{2}80° + \sin^{2}10°

is

0
1
2
$√3/2$

Solution:

\Given:

\tan^ 2 70° \tan^ 2 20°+\sin ^{2} 80°+\sin ^{2} 10°

\Concept \used:

\we \know \that,

\tan (\π/ 2-\θ)=\cot \θ

also,

\sin (\π/ 2-\θ)=\cos \θ

\Formula \used:

\cot \θ\tan \θ=1

\cos ^{2} \θ+\sin ^{2} \θ=1

\Calculation

:

\tan 70° \tan 20°+\sin ^{2} 80°+\sin ^{2} 10°

\⇒\tan (\π/ 2-20°) \tan 20°+\sin ^{2}(\π/ 2-10°)+\sin ^{2} 10°

\⇒\cot 20° \tan 20^°+\(\cos ^{2} 10^°+\sin ^{2} 10°)

\⇒1+1

⇒2

∴\The \value \is 2 .

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