$Choose the correct answer of the following question : \sec 70 ° \sin 20 ° + \cos 20 ° cosec 70 ° = ? (a) 0 (b) 1 (c) - 1 (d) 2$

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Solution

$\sec 70 ° \sin 20 ° + \cos 20 ° cosec 70 ° = cosec (90 ° - 70 °) \sin 20 ° + \cos 20 ° \sec (90 ° - 70 °) = cosec 20 ° \sin 20 ° + \cos 20 ° \sec 20 ° = \frac{1}{\sin 20 °} \times \sin 20 ° + \cos 20 ° \times \frac{1}{\cos 20 °} = 1 + 1 = 2 Hence, the correct answer is option (d) .$

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