Question : $2(\sin 1^{\circ}× \sec 89^{\circ} ) + 3 (\cos 11^{\circ} × \operatorname{cosec} 79^{\circ}) + 5 (\tan 21^{\circ} × \tan 69^{\circ})$ = ?
Option 1: 11
Option 2: 12
Option 3: 20
Option 4: 10
Correct Answer: 10
Solution :
$2(\sin 1^{\circ}× \sec 89^{\circ} ) + 3 (\cos 11^{\circ} × \operatorname{cosec} 79^{\circ}) + 5 (\tan 21^{\circ} × \tan 69^{\circ})$
= $2(\frac{\sin 1^{\circ}}{ \cos 89^{\circ}} ) + 3 (\frac{\cos 11^{\circ}}{ \sin 79^{\circ}}) + 5 (\frac{\tan 21^{\circ} }{\cot 69^{\circ}})$
= $2(\frac{\sin 1^{\circ}}{ \sin(90^{\circ}- 89^{\circ})} ) + 3 (\frac{\cos 11^{\circ}}{ \cos (90^{\circ}-79^{\circ})}) + 5 (\frac{\tan 21^{\circ} }{\tan (90^{\circ}-69^{\circ})})$
= $2(\frac{\sin 1^{\circ}}{ \sin 1^{\circ}} ) + 3 (\frac{\cos 11^{\circ}}{\cos 11^{\circ}}) + 5 (\frac{\tan 21^{\circ} }{\tan 21^{\circ}})$
= $ 2 + 3 + 5$
= $10$
Hence, the correct answer is 10.
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