Question

Solve : $\frac{\sin {65}^o}{\cos {25}^o}+\frac{\cos {32}^o}{\sin {58}^o}-\sin {28}^o\sec {62}^o+{\text{cosec}}^2{30}^o$

Answer 1

$\frac{\sin 65}{\cos 25}+\frac{\cos 32}{\sin 58}-\sin 28\sec 62+{\csc }^{2}30$

$=\frac{\sin (90-25)}{\cos 25}+\frac{\cos 32}{\sin (90-32)}-\sin 28\sec (90-28)+2^2$

$=\frac{\cos 25}{\cos 25}+\frac{\cos 32}{\cos 32}-\sin 28\csc 28+2^2$

$=1+1-1+4$

$=5$

$\frac{\sin 65}{\cos 25}+\frac{\cos 32}{\sin 58}-\sin 28\sec 62+{\csc }^{2}30=5$