Show that: sin 42° sec 48° + cos 42° cos ec48° = 2 - Vidyadip

Question

Show that:
sin 42° sec 48° + cos 42° cos ec48° = 2

✓

Answer

sin 42° sec 48° + cos 42° cos ec48° = 2
consider sin42° sec48° + cos42° cosec48°
⇒ sin42° sec(90° - 42°) + cos42° cosec(90° - 42°)
⇒ sin42° cosec42° + cos42° sec42°
$\Rightarrow \sin 42^{\circ}, \frac{1}{\sin 42^{\circ}+} \frac{\cos 42^{\circ} 1}{\cos 42^{\circ}}$
⇒ 1+ 1 = 2

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