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Haryana Police Constable Model Paper 1

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Question : 24 of 100

Marks: +1, -0

The value of

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

is

0
1
2
$\frac{\sqrt{3}}{2}$

Solution:

\text{Given: }

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

\text{Concept used: }

\text{we know that, }

\tan\left(\frac{\pi}{2} - \theta\right) = \cot \theta

also,

\sin\left(\frac{\pi}{2} - \theta\right) = \cos \theta

\text{Formula used:}

\cot \theta \tan \theta = 1

\cos^{2} \theta + \sin^{2} \theta = 1

\text{Calculation}

:

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

\Rightarrow \tan\left(\frac{\pi}{2} - 20^\circ\right) \tan 20^\circ + \sin^{2}\left(\frac{\pi}{2} - 10^\circ\right) + \sin^{2} 10^\circ

\Rightarrow \cot 20^\circ \tan 20^\circ + \left(\cos^{2} 10^\circ + \sin^{2} 10^\circ\right)

\Rightarrow 1 + 1

\Rightarrow 2

\therefore \text{The value is } 2.

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