Question

Evaluate the value of the following expression.
$A=\frac{cos{58}^{\circ }}{sin{32}^{\circ }}-\frac{cos{38}^{\circ }cosec{52}^{\circ }}{tan{18}^{\circ }tan{35}^{\circ }tan{72}^{\circ }tan{55}^{\circ }}$

• A. \N

Answer 1

The correct option is A 0.0
Using complementary angles property,

$cos{58}^{\circ }=cos(90-{32}^{\circ })=sin{32}^{\circ }$

Similarly,

$cos{38}^{\circ }=cos({90}^{\circ }-{52}^{\circ })=sin{52}^{\circ }$

$tan{18}^{\circ }=tan({90}^{\circ }-{72}^{\circ })=cot{72}^{\circ }$

$tan{35}^{\circ }=tan({90}^{\circ }-{55}^{\circ })=cot{55}^{\circ }$

$A=\frac{cos{58}^{\circ }}{sin{32}^{\circ }}-\frac{cos{38}^{\circ }cosec{52}^{\circ }}{tan{18}^{\circ }tan{35}^{\circ }tan{72}^{\circ }tan{55}^{\circ }}$

$A=\frac{sin{32}^{\circ }}{sin{32}^{\circ }}-\frac{sin{52}^{\circ }cosec{52}^{\circ }}{cot{72}^{\circ }cot{55}^{\circ }tan{72}^{\circ }tan{55}^{\circ }}$

$=1-1$

$=0$