Page 41 - mathsvol1ch1to3ans

41

15 12 π π
1. If sin x = and cos y = , 0 < x < , 0 < y < d ,
17 13 2 2
Solution:Let us first find the values of sin(y) and cos(x).
s
2
12 5
sin(y) = 1 − = .
13 13
s
2
15 8
cos(x) = 1 − = .
17 17
180 40 220
Not For Sale - Veeraragavan C S veeraa1729@gmail.com
(i) sin(x + y) = sin(x) cos(y) + sin(y)cos(x) = + . =
221 221 221
96 75 171
(ii) cos(x − y) = cos(x) cos(y) + sin(x)sin(y) = + =
221 221 221

15 5
+
tan(x) + tan(y) 8 12 220
(iii) tan(x + y) = = =
1 − tan(x) tan(y) 75 21
1 −
96
3 9 π π
2. If sin A = and cos B = , 0 < A < , 0 < B < ,
5 41 2 2
4 40
Solution: cos(A) = and sin(B) =
5 41
27 160 187
(i) sin(A + B) = sin(A) cos(B) + cos(A) sin(B) = + =
205 205 205
36 120 156
(ii) cos(A − B) = cos(A) cos(B) + sin(A) sin(B) = + =
205 205 205
4 3π 24 3π
3. Find cos(x − y), given that cos x = − with π < x < and sin y = − with π < y < .
5 2 25 2
3 7
Solution:sin x = − and cos y = −
5 25

28 72 110 22
cos(x − y) = cos x cos y + sin x sin y = + = = .
125 125 125 25
8 π 24 3π
4. Find sin(x − y), given that sin x = with 0 < x < and cos y = − with π < y < .
17 2 25 2
15 7
Solution:cos x = and sin y = −
17 25
192 85 107
sin(x − y) = sin x cos y − cos x sin y = − + =
425 425 425
7π
5. Find the value of (i) cos 105 ◦ (ii) sin 105 ◦ (iii) tan .
12
Solution: