(Q14)Evaluate the following
cos 45°
sec 30° + cosec 60°
 .

We know that

cos 45° =
1
√
 , sec 30° =
2
√
 , cosec 60° =
2
√
∴
cos 45°
sec 30° + cosec 60°
=
1
√
2
√
+
2
√
 =
1
√
2 +
√
 =
1
√
√
 =
1
√
 ×
√
 =
√
√2
∴
cos 45°
sec 30° + cosec 60°
 =
√
√2