Solution :

(a) Given expression = $ $

$

n 45

1 n 45

1 n (^452)
2
2
ta
si
si



= () [ I n 45 1 ]
2
1
1 n 45
2
1
1
2
1
1
2
2
2

̧
¹
·
̈
©
§
̧
¹
·
̈
©
§
si $ ta $
= 1
2
1
1
2
1
1



= 1
2
3
2
1
 = 1
3
1
 =
3
4
(b) Given expression = cot 90 $˜tan 0 $˜sec 30 $˜cosec 60 $
= 0
3
2
3
2
0 ˜ 0 ˜ ˜
[
3
2
s 60
3
2
cot 90 $ 0 ,tan 0 $ 0 ,sec 30 $ ,coec $ ]
(c) Given expression = sin 60 $˜cos 30 $cos 60 $˜sin 30 $

2
1
2
1
2
3
2
3
˜  ˜
[
2
1
,sin 30 cos 60
2
3
sin 60 $ cos 30 $ $ $ ]

4
1
4
3
 =
4
4
= 1
(d) Given expression = $ $
$
sin 60
1 sin 60
1 tan (^602)
2
2




2
2
2
2
3
1 3
1 3
̧ ̧
¹
·
̈ ̈
©
§




4
3
1 3
1 3




4
3
4
2



4
1
4
2 3
 
Example 2.
(a) If 2 cos(AB) 1 , 2 sin(AB) 3 and A,B are acute angles, find the
values of AandB.