Prove that: 48^ 42^ + 48^ 42^ =2 - Vidyadip

Question

Prove that:$\sin48^\circ\sec42^\circ+\cos48^\circ\text{cosec }42^\circ=2$

✓

Answer

$\text{L.H.S}=\sin48^\circ\sec42^\circ+\cos48^\circ\text{cosec }42^\circ$
$=\sin48\sec(90^\circ-48^\circ)+\cos48^\circ\text{cosec }(90^\circ-48^\circ)$
$=\sin48^\circ\cdot\text{cosec }48^\circ+\cos48^\circ\cdot\sec48^\circ$
$=\sin48^\circ\times\frac{1}{\sin48^\circ}+\cos48^\circ\times\frac{1}{\cos48^\circ}$
$=1+1$
$=2$
$=\text{R.H.S}$

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