sec 17 ∘ cosec 73 ∘ + tan 68 ∘ cot 22 ∘ − [ cos 2 44 ∘ + cos 2 46 ∘ ] = ___. Options: A . &nbsp 0 B . &nbsp -1 C . &nbsp 2 D . &nbsp 1

Answer: Option D : D sec 17 ∘ cosec 73 ∘ + tan 68 ∘ cot 22 ∘ − [ cos 2 44 ∘ + cos 2 46 ∘ ] = sec 17 ∘ cosec ( 90 ∘ − 17 ∘ ) + tan 68 ∘ cot ( 90 ∘ − 68 ∘ ) − [ cos 2 44 ∘ + cos 2 ( 90 ∘ − 44 ∘ ) ] = sec 17 ∘ sec 17 ∘ + tan 68 ∘ tan 68 ∘ − [ cos 2 44 ∘ + sin 2 44 ∘ ] ....(complementary angles) = 1 + 1 − 1 = 1

sec 17∘cosec 73∘+tan 68∘cot 22∘

Question

$\frac{sec 17^{\circ}}{cosec 73^{\circ}} + \frac{tan 68^{\circ}}{cot 22^{\circ}} - [{cos}^{2} 44^{\circ} + {cos}^{2} 46^{\circ}] =$ ___.

Options:

A . 0

B . -1

C . 2

D . 1

Answer: Option D
:
D

$\frac{sec 17^{\circ}}{cosec 73^{\circ}} + \frac{tan 68^{\circ}}{cot 22^{\circ}} - [{cos}^{2} 44^{\circ} + {cos}^{2} 46^{\circ}]$
$= \frac{sec 17^{\circ}}{cosec (90^{\circ} - 17^{\circ})} + \frac{tan 68^{\circ}}{cot (90^{\circ} - 68^{\circ})} - [{cos}^{2} 44^{\circ} + {cos}^{2} (90^{\circ} - 44^{\circ})]$
$= \frac{sec 17^{\circ}}{sec 17^{\circ}} + \frac{tan 68^{\circ}}{tan 68^{\circ}} - [{cos}^{2} 44^{\circ} + {sin}^{2} 44^{\circ}]$ ....(complementary angles)
$= 1 + 1 - 1$
$= 1$