Question

Find the value of
$sin$ ${43}^{\circ }$ $\times$ $\frac{1}{cos{47}^{\circ }}$ $\times$ $sec$ ${63}^{\circ }$ $\times$ $\frac{1}{cosec{27}^{\circ }}$

• A. $se{c}^2{63}^{\circ }$
• B. $cosec$ ${27}^{\circ }$
• C. 1
• D. 2

Answer 1

The correct option is C 1

$\because$ $sin$ ${43}^{\circ }$ = $sin$ (${90}^{\circ }-{47}^{\circ }$) = $cos{47}^{\circ }$
and
$sec$ ${63}^{\circ }$ = $sec$ (${90}^{\circ }-{27}^{\circ }$) = $cosec{27}^{\circ }$

$\therefore$
$sin$ ${43}^{\circ }$ $\times$ $\frac{1}{cos{47}^{\circ }}$ $\times$ $sec$ ${63}^{\circ }$ $\times$ $\frac{1}{cosec{27}^{\circ }}$

$=cos$ ${47}^{\circ }$$\times$$\frac{1}{cos{47}^{\circ }}$$\times$$cosec$ ${27}^{\circ }$$\times$$\frac{1}{cosec{27}^{\circ }}$

=1