sec 70° sin 20° + cos 20° cosec 70° = ?
(a) 0
(b) 1
(c) 2
(d) –2

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Solution

$\sec 70 ° \sin 20 ° + \cos 20 ° cosec 70 ° = \sec (90 ° - 20 °) \sin 20 ° + \cos 20 ° cosec (90 ° - 20 °) = cosec 20 ° \sin 20 ° + \cos 20 ° \sec 20 ° (∵ \sec (90 ° - θ) = cosec θ and cosec (90 ° - θ) = \sec θ) = \frac{1}{\sin 20 °} \sin 20 ° + \cos 20 ° \frac{1}{\cos 20 °} (∵ cosec θ = \frac{1}{\sin θ} and \sec θ = \frac{1}{\cos θ}) = 1 + 1 = 2 Hence, the correct option is (c) .$

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