EduSahara™ Assignment
Name : Trigonometry Miscellaneous
Chapter : Trigonometrical Identities
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
Which of the following are true?
a)
If
sin
H
= 0 , then
cos
H
= 1 or
cos
H
= -1
b)
The value of
cot
H
is always less than 1
c)
cos
H
is the abbrieviation for
cosec
H
d)
The value of
sin
H
is always less than 1
e)
The value of
tan
H
is always less than 1
(i)
{c,d,a}
(ii)
{a,d}
(iii)
{b,a}
(iv)
{e,b,a}
(v)
{c,d}
Question
2
2.
For angle values from 0° to 90°, which of the following are true?
a)
The sine value of the angle increases
b)
The product of the sine and cosine values remains a constant
c)
The cotangent value of the angle increases
d)
The cosine value of the angle increases
e)
The tangent value of the angle increases
f)
The sum of the squares of the sine and cosine values remains a constant
(i)
{c,a,e}
(ii)
{a,e,f}
(iii)
{b,a}
(iv)
{d,b,f}
(v)
{c,e}
Question
3
3.
Which of the following are true?
a)
cos
(
D
+
E
)
=
cos
D
+
cos
E
b)
The cotangent of an angle is the reciprocal of the tangent of the angle.
c)
tan
D
= tan
✕
D
d)
sin
(
D
+
E
)
=
sin
D
+
sin
E
e)
The cosine value of an angle is the reciprocal of the sine of the angle.
f)
The cosecant of an angle is the reciprocal of the secant of the angle
(i)
{c,b}
(ii)
{f,b}
(iii)
{d,e,b}
(iv)
{b}
(v)
{a,b}
Question
4
4.
Which of the following are true?
a)
The value of
cos
θ
increases as
θ
increases from
0°
to
90°
b)
The value of
sin
θ
increases as
θ
increases from
0°
to
90°
c)
cos
(
G
+
H
)
=
cos
G
+
cos
H
d)
tan
(
G
+
H
)
=
tan
G
+
tan
H
e)
sin
θ
=
cos
θ
for all
θ
f)
sin
(
G
+
H
)
=
sin
G
+
sin
H
g)
tan
θ
=
cot
θ
for no value of
θ
(i)
{b}
(ii)
{c,b}
(iii)
{f,b}
(iv)
{d,e,b}
(v)
{a,b}
Question
5
5.
If
sin
2
F
=
2
sin
F
, then
F
=
(i)
0°
(ii)
60°
(iii)
30°
(iv)
90°
(v)
45°
Question
6
6.
If
sin
(
C
+
D
)
=
1
2
√
3
and
sin
(
C
−
D
)
=
1
2
,
find
C
&
D
(i)
C
=
46°
,
D
=
16°
(ii)
C
=
45°
,
D
=
15°
(iii)
C
=
47°
,
D
=
17°
(iv)
C
=
43°
,
D
=
13°
(v)
C
=
44°
,
D
=
14°
Question
7
7.
If
tan
(
H
+
I
)
=
√
3
and
tan
(
H
−
I
)
=
√
1
3
,
find
H
&
I
(i)
H
=
45°
,
I
=
15°
(ii)
H
=
44°
,
I
=
14°
(iii)
H
=
46°
,
I
=
16°
(iv)
H
=
43°
,
I
=
13°
(v)
H
=
47°
,
I
=
17°
Question
8
8.
In
△EFG
, right angled at
F
,
if
tan
E
=
1
2
,
find
sin
E
cos
G
+
cos
E
sin
G
(i)
1
5
√
5
(ii)
√
5
(iii)
1
2
√
5
(iv)
1
(v)
2
5
√
5
Question
9
9.
In
△HIJ
, right angled at
I
,
if
tan
H
=
1
3
,
find
cos
H
cos
J
−
sin
H
sin
J
(i)
√
10
(ii)
1
3
√
10
(iii)
3
10
√
10
(iv)
0
(v)
1
10
√
10
Question
10
10.
If
cot
θ
=
1
2
, find
(
1
+
sin
θ
)
(
1
−
sin
θ
)
(
1
−
cos
θ
)
(
1
+
cos
θ
)
(i)
3
4
(ii)
1
6
(iii)
1
4
(iv)
(
-1
4
)
(v)
1
2
Question
11
11.
If
tan
θ
=
2
5
, find
(
1
+
cos
θ
)
(
1
−
cos
θ
)
(
1
+
sin
θ
)
(
1
−
sin
θ
)
(i)
2
25
(ii)
6
25
(iii)
4
27
(iv)
4
23
(v)
4
25
Question
12
12.
Find the value of
(
1
+
sin
θ
)
(
cos
θ
)
+
(
cos
θ
)
(
1
+
sin
θ
)
(i)
2
sin
θ
(ii)
2
cosec
θ
(iii)
2
cos
θ
(iv)
2
sec
θ
Question
13
13.
Find the value of
4
sec
2
θ
−
4
tan
2
θ
(i)
1
(ii)
2
(iii)
6
(iv)
0
(v)
4
Question
14
14.
If
tan
θ
+
cot
θ
=
3
, find
tan
2
θ
+
cot
2
θ
(i)
4
(ii)
8
(iii)
7
(iv)
10
(v)
6
Question
15
15.
If
tan
θ
−
cot
θ
=
5
, find
tan
2
θ
+
cot
2
θ
(i)
26
(ii)
28
(iii)
27
(iv)
29
(v)
24
Question
16
16.
If
sin
5
x
=
cos
(
(
x
+
60
)
)
, then
x
=
(i)
7
(ii)
4
(iii)
6
(iv)
2
(v)
5
Question
17
17.
If
cos
6
x
=
sin
(
(
x
+
34
)
)
, then
x
=
(i)
5
(ii)
7
(iii)
8
(iv)
9
(v)
10
Question
18
18.
If
tan
4
x
=
cot
(
(
x
+
45
)
)
, then
x
=
(i)
10
(ii)
9
(iii)
6
(iv)
8
(v)
11
Question
19
19.
If
cot
5
x
=
tan
(
(
x
+
12
)
)
, then
x
=
(i)
15
(ii)
14
(iii)
13
(iv)
10
(v)
12
Question
20
20.
If
sec
4
x
=
cosec
(
(
x
+
40
)
)
, then
x
=
(i)
10
(ii)
12
(iii)
8
(iv)
11
(v)
9
Question
21
21.
If
cosec
5
x
=
sec
(
(
x
+
6
)
)
, then
x
=
(i)
12
(ii)
15
(iii)
13
(iv)
14
(v)
17
Question
22
22.
If
V
,
W
and
X
are the interior angles of a triangle, then
sin
(
V + W
2
)
=
(i)
cos
(
X
2
)
(ii)
sin
(
V
2
)
(iii)
sin
X
(iv)
cos
(
V
2
)
(v)
sin
(
X
2
)
Question
23
23.
Which of the following are true?
a)
cos
56°
=
sin
56°
b)
sin
30°
=
cos
30°
c)
sin
31°
=
cos
59°
d)
sin
44°
=
cos
46°
e)
tan
49°
=
cot
41°
f)
sin
39°
=
cos
51°
g)
sec
29°
=
cosec
61°
(i)
{c,d,e,f,g}
(ii)
{b,d}
(iii)
{a,b,e}
(iv)
{a,f,g}
(v)
{a,c}
Question
24
24.
Which of the following are true?
a)
cosec
90°
is not defined
b)
tan
0°
is not defined
c)
cot
0°
is not defined
d)
tan
90°
is not defined
e)
cot
90°
is not defined
f)
sec
0°
is not defined
g)
cosec
0°
is not defined
h)
sec
90°
is not defined
(i)
{a,h,c}
(ii)
{c,d,g,h}
(iii)
{b,d}
(iv)
{e,f,g}
(v)
{a,c}
Question
25
25.
Which of the following are true?
a)
cot
θ
=
1
sec
θ
b)
cosec
θ
=
1
sin
θ
c)
tan
θ
=
1
cot
θ
d)
sec
θ
=
1
sin
θ
e)
cos
θ
=
1
cosec
θ
f)
sec
θ
=
1
cos
θ
(i)
{e,a,f}
(ii)
{a,b}
(iii)
{b,c,f}
(iv)
{d,b,c}
(v)
{d,c}
Question
26
26.
Which of the following are true?
a)
cos
0°
=
1
b)
sin
0°
=
1
c)
sin
90°
=
1
d)
tan
90°
=
1
e)
sin
45°
=
1
f)
tan
0°
=
1
g)
cos
45°
=
1
h)
cos
90°
=
1
(i)
{g,c,a}
(ii)
{e,f,a}
(iii)
{d,c}
(iv)
{b,a}
(v)
{a,c}
Question
27
27.
Which of the following are true?
a)
cos
0°
=
0
b)
tan
0°
=
0
c)
cos
90°
=
0
d)
tan
90°
=
0
e)
sin
45°
=
0
f)
sin
90°
=
0
g)
cos
45°
=
0
h)
sin
0°
=
0
(i)
{a,b}
(ii)
{e,f,h}
(iii)
{b,c,h}
(iv)
{d,c}
(v)
{g,b,c}
Question
28
28.
Which of the following are true?
a)
cosec
(
90
+
θ
)
=
−
cosec
θ
b)
cosec
(
90
+
θ
)
=
sec
θ
c)
sec
(
90
+
θ
)
=
−
cosec
θ
d)
cot
(
90
+
θ
)
=
−
tan
θ
e)
sec
(
90
+
θ
)
=
−
sec
θ
f)
cot
(
90
+
θ
)
=
−
cot
θ
(i)
{e,b,c}
(ii)
{b,c,d}
(iii)
{e,c}
(iv)
{f,a,d}
(v)
{a,b}
Question
29
29.
Which of the following are true?
a)
cos
(
90
+
θ
)
=
−
cos
θ
b)
tan
(
90
+
θ
)
=
−
cot
θ
c)
sin
(
90
+
θ
)
=
cos
θ
d)
cos
(
90
+
θ
)
=
−
sin
θ
e)
tan
(
90
+
θ
)
=
−
tan
θ
f)
sin
(
90
+
θ
)
=
−
sin
θ
(i)
{e,c}
(ii)
{a,b}
(iii)
{f,a,d}
(iv)
{b,c,d}
(v)
{e,b,c}
Question
30
30.
Which of the following are true?
a)
sin
(
−
θ
)
=
−
sin
θ
b)
cos
(
−
θ
)
=
−
cos
θ
c)
tan
(
−
θ
)
=
tan
θ
d)
sin
(
−
θ
)
=
sin
θ
e)
cos
(
−
θ
)
=
cos
θ
f)
tan
(
−
θ
)
=
−
tan
θ
(i)
{c,e}
(ii)
{d,b,f}
(iii)
{b,a}
(iv)
{a,e,f}
(v)
{c,a,e}
Question
31
31.
Which of the following are true?
a)
sec
(
−
θ
)
=
sec
θ
b)
cot
(
−
θ
)
=
cot
θ
c)
cot
(
−
θ
)
=
−
cot
θ
d)
sec
(
−
θ
)
=
−
sec
θ
e)
cosec
(
−
θ
)
=
cosec
θ
f)
cosec
(
−
θ
)
=
−
cosec
θ
(i)
{d,c}
(ii)
{e,b,f}
(iii)
{d,a,c}
(iv)
{b,a}
(v)
{a,c,f}
Question
32
32.
If
u
=
cos
θ
+
sin
θ
,
v
=
cos
θ
sin
θ
then
(i)
(
u
2
+
v
2
)
=
1
(ii)
u
2
=
(
2
v
+
1
)
(iii)
(
u
2
+
v
2
)
=
0
(iv)
u
2
=
(
−
2
v
+
1
)
(v)
(
u
2
−
v
2
)
=
1
Question
33
33.
If
w
=
cos
θ
+
sin
θ
,
x
=
cos
θ
−
sin
θ
then
(i)
(
w
2
+
x
2
)
=
1
(ii)
(
w
2
+
x
2
)
=
2
(iii)
(
w
2
−
x
2
)
=
2
(iv)
(
w
2
−
x
2
)
=
1
(v)
(
w
2
+
x
2
)
=
0
Question
34
34.
a)
(
s
+
t
)
2
=
d
2
b)
2
s
t
=
d
2
sin
2
θ
c)
(
s
2
+
t
2
)
=
d
2
d)
(
s
2
−
t
2
)
=
d
2
e)
s
2
t
2
=
tan
2
θ
(i)
{d,c}
(ii)
{a,d,e}
(iii)
{b,c,e}
(iv)
{a,b}
(v)
{a,b,c}
Question
35
35.
If
e
=
y
cos
θ
+
z
sin
θ
and
f
=
y
sin
θ
−
z
cos
θ
, then
(i)
e
f
=
y
z
(ii)
(
e
2
+
f
2
)
=
(
y
2
+
z
2
)
(iii)
(
e
2
−
f
2
)
=
(
y
2
−
z
2
)
(iv)
(
y
2
+
e
2
)
=
(
z
2
+
f
2
)
Assignment Key
1) (ii)
2) (ii)
3) (iv)
4) (i)
5) (i)
6) (ii)
7) (i)
8) (iv)
9) (iv)
10) (iii)
11) (v)
12) (iv)
13) (v)
14) (iii)
15) (iii)
16) (v)
17) (iii)
18) (ii)
19) (iii)
20) (i)
21) (iv)
22) (i)
23) (i)
24) (ii)
25) (iii)
26) (v)
27) (iii)
28) (ii)
29) (iv)
30) (iv)
31) (v)
32) (ii)
33) (ii)
34) (iii)
35) (ii)
