MCQExams
0:0:4
CBSE
JEE
NTSE
NEET
Practice
Homework
×
CBSE Questions for Class 10 Maths Introduction To Trigonometry Quiz 13 - MCQExams.com
CBSE
Class 10 Maths
Introduction To Trigonometry
Quiz 13
If
cot
θ
+
tan
θ
=
x
cot
θ
+
tan
θ
=
x
and
sec
θ
−
cos
θ
=
y
sec
θ
−
cos
θ
=
y
, then
Report Question
0%
sin
θ
cos
θ
=
1
x
sin
θ
cos
θ
=
1
x
0%
sin
θ
tan
θ
=
y
sin
θ
tan
θ
=
y
0%
(
x
2
y
)
2
/
3
=
1
(
x
2
y
)
2
/
3
=
1
0%
(
x
2
y
)
1
/
3
+
(
x
y
2
)
1
/
3
=
1
(
x
2
y
)
1
/
3
+
(
x
y
2
)
1
/
3
=
1
Explanation
cot
θ
+
tan
θ
=
x
⇒
cos
θ
sin
θ
+
sin
θ
cos
θ
=
x
cot
θ
+
tan
θ
=
x
⇒
cos
θ
sin
θ
+
sin
θ
cos
θ
=
x
1
sin
θ
cos
θ
=
x
⇒
sin
θ
cos
θ
=
1
x
1
sin
θ
cos
θ
=
x
⇒
sin
θ
cos
θ
=
1
x
...(1)
s
e
c
θ
−
cos
θ
=
y
⇒
1
cos
θ
−
cos
θ
=
y
s
e
c
θ
−
cos
θ
=
y
⇒
1
cos
θ
−
cos
θ
=
y
⇒
1
−
cos
2
θ
cos
θ
=
y
⇒
sin
2
θ
cos
θ
=
y
⇒
1
−
cos
2
θ
cos
θ
=
y
⇒
sin
2
θ
cos
θ
=
y
⇒
sin
θ
tan
θ
=
y
⇒
sin
θ
tan
θ
=
y
...(2)
From (1) and (2)
x
2
y
=
1
sin
2
θ
cos
2
θ
×
sin
2
θ
cos
θ
=
1
cos
3
θ
=
s
e
c
3
θ
y
2
x
=
sin
4
θ
cos
2
θ
×
1
sin
θ
cos
θ
=
tan
3
θ
(
x
2
y
)
1
3
+
(
y
2
x
)
1
3
=
sec
θ
+
tan
θ
If
x
=
sin
3
p
cos
2
p
,
y
=
cos
3
p
sin
2
p
and
sin
p
+
cos
p
=
1
2
, then
x
+
y
is equal to
Report Question
0%
75
18
0%
44
9
0%
79
18
0%
48
9
Explanation
Given
x
=
sin
3
p
cos
2
p
,
y
=
cos
3
p
sin
2
p
; and
sin
p
+
cos
p
=
1
2
Consider,
x
+
y
=
sin
3
p
cos
2
p
+
cos
3
p
sin
2
p
⇒
x
+
y
=
sin
5
p
+
cos
5
p
sin
2
p
cos
2
p
=
sin
3
p
(
1
−
cos
2
p
)
+
cos
3
p
(
1
−
sin
2
p
)
sin
2
p
cos
2
p
=
sin
3
p
+
cos
3
p
−
sin
2
p
cos
2
p
(
sin
p
+
cos
p
)
sin
2
p
cos
2
p
=
(
sin
p
+
cos
p
)
3
−
3
sin
p
cos
p
(
sin
p
+
cos
p
)
−
sin
2
p
cos
2
p
(
sin
p
+
cos
p
)
sin
2
p
cos
2
p
.....(1)
Since
(
sin
p
+
c
o
s
p
)
2
=
sin
2
p
+
cos
2
p
+
2
sin
p
cos
p
⇒
sin
p
cos
p
=
−
3
4
So, using in (1),
x
+
y
=
1
8
+
9
16
−
9
32
9
16
=
79
18
In the figure given
∠
A
B
D
=
∠
P
Q
D
=
∠
C
D
Q
=
π
2
. If
A
B
=
x
.
P
Q
=
z
and
C
D
=
y
, then which one of the following is correct?
Report Question
0%
1
x
+
1
y
=
1
z
0%
1
x
+
1
z
=
1
y
0%
1
z
+
1
y
=
1
x
0%
1
x
+
1
y
=
2
z
Find the relation obtained by eliminating
θ
from the equation
x
=
a
cos
θ
+
b
sin
θ
and
y
=
a
sin
θ
−
b
cos
θ
Report Question
0%
x
2
+
y
2
=
a
2
−
b
2
0%
x
2
−
y
2
=
a
2
+
b
2
0%
x
2
−
y
2
=
a
2
−
b
2
0%
x
2
+
y
2
=
a
2
+
b
2
Explanation
Given,
x
=
a
cos
θ
+
b
sin
θ
and
y
=
a
sin
θ
−
b
cos
θ
Squaring them and adding we get
x
2
+
y
2
=
a
2
cos
2
θ
+
b
2
sin
2
θ
+
2
a
b
cos
θ
sin
θ
+
a
2
sin
2
θ
+
b
2
cos
2
θ
−
2
a
b
cos
θ
sin
θ
⇒
x
2
+
y
2
=
a
2
cos
2
θ
+
b
2
sin
2
θ
+
a
2
sin
2
θ
+
b
2
cos
2
θ
⇒
x
2
+
y
2
=
a
2
(
cos
2
θ
+
sin
2
θ
)
+
b
2
(
sin
2
θ
+
cos
2
θ
)
⇒
x
2
+
y
2
=
a
2
+
b
2
Which one of the following when simplified is not equal to one?
Report Question
0%
tan
18
∘
×
tan
36
∘
×
tan
54
∘
×
tan
72
∘
0%
sin
2
19
∘
+
sin
2
71
∘
0%
2
sin
62
∘
cos
28
∘
−
sec
42
∘
cosec
48
∘
0%
None of these
Explanation
(1)
tan
18
∘
×
tan
36
∘
×
tan
54
∘
×
tan
72
∘
=
tan
18
∘
×
tan
(
90
−
54
)
∘
×
tan
54
∘
×
tan
(
90
−
18
)
∘
=
tan
18
∘
×
cot
54
∘
×
tan
54
∘
×
cot
18
∘
=
1
(2)
sin
2
19
∘
+
sin
2
71
∘
=
sin
2
19
∘
+
sin
2
(
90
−
19
)
∘
=
sin
2
19
∘
+
cos
2
19
∘
=
1
(3)
2
sin
62
∘
cos
28
∘
−
sec
42
∘
c
o
s
e
c
48
∘
=
2
sin
62
∘
cos
(
90
−
62
)
∘
−
sec
42
∘
c
o
s
e
c
(
90
−
42
)
∘
=
2
sin
62
∘
sin
62
∘
−
sec
42
∘
sec
42
∘
=
2
−
1
=
1
Thus, all are equal to one. Hence, none of these is the answer.
If
1
−
c
o
s
x
c
o
s
x
(
1
+
c
o
s
x
)
=
s
i
n
α
c
o
s
x
−
2
1
+
c
o
s
x
, then
α
=
Report Question
0%
π
8
0%
π
4
0%
Both A and B
0%
None of the above
c
o
t
θ
+
c
o
s
e
c
θ
−
1
c
o
t
θ
−
c
o
s
e
c
θ
+
1
is equal to:
Report Question
0%
1
+
c
o
s
θ
s
i
n
θ
0%
s
i
n
θ
1
+
c
o
s
θ
0%
s
i
n
θ
1
−
c
o
s
θ
0%
1
−
c
o
s
θ
s
i
n
θ
If
cos
P
=
1
7
and
cos
Q
=
13
14
, P and Q both are acute angle then the value of
P
−
Q
will be?
Report Question
0%
45
o
0%
30
o
0%
75
o
0%
60
o
sin
48
0
.
sin
12
0
=
Report Question
0%
1
+
√
5
8
0%
1
−
√
5
8
0%
√
5
+
1
8
0%
√
5
−
1
8
1
+
c
o
s
e
c
π
4
+
c
o
s
e
c
π
8
+
c
o
s
e
c
π
16
=
Report Question
0%
c
o
t
π
8
0%
c
o
t
π
16
0%
c
o
t
π
32
0%
c
o
s
e
c
2
π
16
sec
8
A
−
1
sec
4
A
−
1
=
Report Question
0%
0
0%
tan
8
A
tan
2
A
0%
cos
8
A
cos
2
A
0%
sin
8
A
sin
2
A
t
a
n
θ
1
−
c
o
t
θ
+
c
o
t
θ
1
−
t
a
n
θ
is equal to:
Report Question
0%
1
+
s
i
n
θ
c
o
s
t
θ
0%
s
i
n
θ
c
o
s
θ
0%
s
e
c
θ
c
o
s
e
c
θ
0%
1
+
s
e
c
θ
c
o
s
e
c
θ
Suppose
I
1
=
∫
π
/
2
0
c
o
s
(
π
s
i
n
2
x
)
d
x
;
I
2
=
∫
π
/
2
0
c
o
s
(
2
π
s
i
n
2
x
)
d
x
a
n
d
I
3
=
∫
π
/
2
0
c
o
s
(
π
s
i
n
x
)
d
x
then
Report Question
0%
I
1
=
0
0%
I
2
+
I
1
=
0
0%
I
1
+
I
2
+
I
3
=
0
0%
I
2
=
I
3
1
+
c
o
s
e
c
π
4
+
c
o
s
e
c
π
8
c
o
s
e
c
π
16
=
Report Question
0%
c
o
t
π
8
0%
c
o
t
π
16
0%
c
o
t
π
32
0%
c
o
s
e
c
2
If
c
o
s
(
80
∘
+
Θ
)
=
s
i
n
(
k
3
)
−
Θ
)
then k=.....
Report Question
0%
81
0%
27
0%
54
0%
9
If the median of a triangle ABC passing through A is perpendicular AB then tanA + 2tanB =
Report Question
0%
1
0%
1
0%
0
0%
None
An angle is increasing at a constant rate. The rate of increase of tan when the angle is
π
/
3
is
Report Question
0%
4 times the increase of sine
0%
8 times the increase of cosine
0%
8 times the increase of sine
0%
4 times the increase of cosine
c
o
s
A
1
+
s
i
n
A
+
c
o
s
A
1
−
s
i
n
A
=
Report Question
0%
2
s
e
c
A
0%
2
c
o
s
A
0%
2
0%
0
The value of
c
o
t
54
0
c
o
t
36
0
+
t
a
n
20
0
c
o
t
70
0
=
.
Report Question
0%
3
0%
1
0%
0
0%
2
In triangle ABC, if
s
i
n
A
c
o
s
B
=
1
4
and
3
t
a
n
A
=
t
a
n
B
then
c
o
t
2
A
is equal to
Report Question
0%
2
0%
3
0%
4
0%
5
If
sec
θ
+
tan
θ
=
x
,
then
sec
θ
=
.
.
.
.
.
.
.
.
.
.
.
.
Report Question
0%
x
2
+
1
x
0%
x
2
+
1
2
x
0%
x
2
−
1
2
x
0%
x
2
−
1
x
c
o
s
θ
s
e
c
θ
+
t
a
n
θ
+
c
o
s
θ
s
e
c
θ
−
t
a
n
θ
=
Report Question
0%
1
0%
c
o
s
θ
0%
s
i
n
θ
0%
2
s
i
n
A
c
o
s
e
c
A
+
c
o
s
A
s
e
c
A
=
Report Question
0%
1
0%
s
i
n
2
A
0%
2
s
i
n
2
A
+
c
o
s
2
A
0%
2
s
e
c
A
If
t
a
n
A
=
√
2
−
1
,
t
h
e
n
t
h
e
v
a
l
u
e
o
f
c
o
s
e
c
.
A
.
s
e
c
A
i
s
e
q
u
a
l
t
o
Report Question
0%
1
√
2
0%
1
√
2
0%
2
√
2
0%
√
3
2
t
a
n
−
1
(
1
+
s
i
n
x
c
o
s
x
)
=
Report Question
0%
π
4
−
x
2
0%
π
4
−
x
0%
π
4
+
x
0%
π
4
+
x
2
0:0:4
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
0
Answered
1
Not Answered
24
Not Visited
Correct : 0
Incorrect : 0
Report Question
×
What's an issue?
Question is wrong
Answer is wrong
Other Reason
Want to elaborate a bit more? (optional)
Practice Class 10 Maths Quiz Questions and Answers
<
>
Support mcqexams.com by disabling your adblocker.
×
Please disable the adBlock and continue.
Thank you.
Reload page