Question

Find the value of $\sin {18}^{\circ }cosec{54}^{\circ }cosec{36}^{\circ }\sec {72}^{\circ }\cos {54}^{\circ }\cos {36}^{\circ }.$

• A. $1$
• B. $0$
• C. $2$
• D. $-1$

Answer 1

The correct option is A $1$

Given expression

$\sin {18}^{\circ }\text{cosec}{54}^{\circ }{\text{cosec36}}^{\circ }\sec {72}^{\circ }\cos {54}^{\circ }\cos {36}^{\circ }$

$\frac{\sin {18}^{\circ }\cos {54}^{\circ }\cos {36}^{\circ }}{\sin {54}^{\circ }\sin {36}^{\circ }\cos {72}^{\circ }}$

$\frac{\sin {18}^{\circ }\cos {54}^{\circ }\cos {36}^{\circ }}{\cos {36}^{\circ }\cos {54}^{\circ }\sin {18}^{\circ }}$

$=1$