RS Aggarwal Solutions: Trigonometric Identities (Exercise 8A) | Mathematics (Maths) Class 10 PDF Download

 Page 1


 
1. (i) 
2 2
1 cos cos 1 e c
(ii)
2 2
1 cot sin 1
Sol:
(i)
=
=
= 1
Hence, LHS = RHS
(ii)
=
=
= 1
Hence, LHS = RHS
2. (i) 
2 2
sec 1 cot 1
(ii)
2 2
1 cos 1 1 s e c e c
(iii)
2 2 2
1 cos tan s e c
Sol:
(i)
=
=
= 1
= RHS
(ii)
=
=
= 1
=RHS
(iii)
=
=
=
=
= RHS
Page 2


 
1. (i) 
2 2
1 cos cos 1 e c
(ii)
2 2
1 cot sin 1
Sol:
(i)
=
=
= 1
Hence, LHS = RHS
(ii)
=
=
= 1
Hence, LHS = RHS
2. (i) 
2 2
sec 1 cot 1
(ii)
2 2
1 cos 1 1 s e c e c
(iii)
2 2 2
1 cos tan s e c
Sol:
(i)
=
=
= 1
= RHS
(ii)
=
=
= 1
=RHS
(iii)
=
=
=
=
= RHS
 
3. (i) 
2
2
1
sin 1
1 tan
(ii)
2 2
1 1
1
1 tan 1 cot
Sol:
(i)
=
=
= 1
= RHS
(ii)
=
=
= 1
= RHS
4. (i) 
2
1 cos 1 cos 1 cos 1
(ii) cos 1 cos cot 1 e c c o s e c
Sol:
(i)
=
=
=
= 1
= RHS
(ii)
=
=
=
=
= 1
= RHS
Page 3


 
1. (i) 
2 2
1 cos cos 1 e c
(ii)
2 2
1 cot sin 1
Sol:
(i)
=
=
= 1
Hence, LHS = RHS
(ii)
=
=
= 1
Hence, LHS = RHS
2. (i) 
2 2
sec 1 cot 1
(ii)
2 2
1 cos 1 1 s e c e c
(iii)
2 2 2
1 cos tan s e c
Sol:
(i)
=
=
= 1
= RHS
(ii)
=
=
= 1
=RHS
(iii)
=
=
=
=
= RHS
 
3. (i) 
2
2
1
sin 1
1 tan
(ii)
2 2
1 1
1
1 tan 1 cot
Sol:
(i)
=
=
= 1
= RHS
(ii)
=
=
= 1
= RHS
4. (i) 
2
1 cos 1 cos 1 cos 1
(ii) cos 1 cos cot 1 e c c o s e c
Sol:
(i)
=
=
=
= 1
= RHS
(ii)
=
=
=
=
= 1
= RHS
 
5. (i) 
2
2
1
cot 1
sin
(ii)
2
2
1
tan 1
cos
(iii)
2
2
1
cos 1
1 cot
Sol:
(i)
=
=
=
= -1
=RHS
(ii)
=
=
=
= -1
= RHS
(iii)
=
=
=1
= RHS
6.
2
1 1
2sec
1 sin 1 sin
Sol:
=
=
=
2
2
cos
=
= RHS
Page 4


 
1. (i) 
2 2
1 cos cos 1 e c
(ii)
2 2
1 cot sin 1
Sol:
(i)
=
=
= 1
Hence, LHS = RHS
(ii)
=
=
= 1
Hence, LHS = RHS
2. (i) 
2 2
sec 1 cot 1
(ii)
2 2
1 cos 1 1 s e c e c
(iii)
2 2 2
1 cos tan s e c
Sol:
(i)
=
=
= 1
= RHS
(ii)
=
=
= 1
=RHS
(iii)
=
=
=
=
= RHS
 
3. (i) 
2
2
1
sin 1
1 tan
(ii)
2 2
1 1
1
1 tan 1 cot
Sol:
(i)
=
=
= 1
= RHS
(ii)
=
=
= 1
= RHS
4. (i) 
2
1 cos 1 cos 1 cos 1
(ii) cos 1 cos cot 1 e c c o s e c
Sol:
(i)
=
=
=
= 1
= RHS
(ii)
=
=
=
=
= 1
= RHS
 
5. (i) 
2
2
1
cot 1
sin
(ii)
2
2
1
tan 1
cos
(iii)
2
2
1
cos 1
1 cot
Sol:
(i)
=
=
=
= -1
=RHS
(ii)
=
=
=
= -1
= RHS
(iii)
=
=
=1
= RHS
6.
2
1 1
2sec
1 sin 1 sin
Sol:
=
=
=
2
2
cos
=
= RHS
 
7. (i) sec 1 sin sec tan 1
(ii) sin 1 tan cos 1 cot sec cos e c
Sol:
(i)
=
=
=
=
= 1
= RHS
(ii)
=
=
=
=
=
=
=
=
=
=RHS
8. (i) 
2
cot
1 cos
1 cos
e c
e c
(ii)
2
tan
1
1
s e c
s e c
Sol:
(i)
=
=
=1+
=
Page 5


 
1. (i) 
2 2
1 cos cos 1 e c
(ii)
2 2
1 cot sin 1
Sol:
(i)
=
=
= 1
Hence, LHS = RHS
(ii)
=
=
= 1
Hence, LHS = RHS
2. (i) 
2 2
sec 1 cot 1
(ii)
2 2
1 cos 1 1 s e c e c
(iii)
2 2 2
1 cos tan s e c
Sol:
(i)
=
=
= 1
= RHS
(ii)
=
=
= 1
=RHS
(iii)
=
=
=
=
= RHS
 
3. (i) 
2
2
1
sin 1
1 tan
(ii)
2 2
1 1
1
1 tan 1 cot
Sol:
(i)
=
=
= 1
= RHS
(ii)
=
=
= 1
= RHS
4. (i) 
2
1 cos 1 cos 1 cos 1
(ii) cos 1 cos cot 1 e c c o s e c
Sol:
(i)
=
=
=
= 1
= RHS
(ii)
=
=
=
=
= 1
= RHS
 
5. (i) 
2
2
1
cot 1
sin
(ii)
2
2
1
tan 1
cos
(iii)
2
2
1
cos 1
1 cot
Sol:
(i)
=
=
=
= -1
=RHS
(ii)
=
=
=
= -1
= RHS
(iii)
=
=
=1
= RHS
6.
2
1 1
2sec
1 sin 1 sin
Sol:
=
=
=
2
2
cos
=
= RHS
 
7. (i) sec 1 sin sec tan 1
(ii) sin 1 tan cos 1 cot sec cos e c
Sol:
(i)
=
=
=
=
= 1
= RHS
(ii)
=
=
=
=
=
=
=
=
=
=RHS
8. (i) 
2
cot
1 cos
1 cos
e c
e c
(ii)
2
tan
1
1
s e c
s e c
Sol:
(i)
=
=
=1+
=
 
= RHS
(ii)
=
=
=
=
= RHS
9.
2
2
tan cot
1 tan
cos e c
Sol:
=RHS
Hence, LHS = RHS
10.
2 2
2 2
tan cot
1
1 tan 1 cot
Sol:
LHS =
=
=
=
= 1
= RHS
Hence, LHS = RHS