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TS EAMCET 10-Sep-2020 Shift 1 Solved Paper
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© examsnet.com
Question : 22
Total: 160
Assertion (A): If A=15°, B=17° and C=13° then
c
o
t
2
A
+
c
o
t
2
B
+
c
o
t
2
C
=
c
o
t
2
A
c
o
t
2
B
c
o
t
2
C
Reason (R): In a ΔPQR,
T
a
n
P
2
T
a
n
Q
2
+
T
a
n
Q
2
T
a
n
R
2
+
T
a
n
P
2
T
a
n
R
2
=
1
(A) is true, (R) is true and (R) is the correct explanation for (A)
(A) is tine, (R) is true but (R) is not the correct explanation for (A)
(A) is true but (R) is false
(A) is false but (R) is true
Validate
Solution:
👈: Video Solution
Reason In
∆
P
Q
R
P
+
Q
+
R
=
180
∘
⇒
P
2
+
Q
2
+
R
2
=
90
∘
⇒
P
2
+
Q
2
=
90
∘
−
R
2
⇒
tan
(
P
2
+
Q
2
)
=
tan
(
90
−
R
2
)
⇒
tan
P
2
+
tan
Q
2
1
−
tan
P
2
tan
Q
2
=
cot
R
2
⇒
(
tan
P
2
+
tan
Q
2
)
tan
R
2
=
1
−
tan
P
2
tan
Q
2
⇒
tan
P
2
tan
Q
2
+
tan
Q
2
tan
R
2
+
tan
R
2
tan
P
2
=
1
So, reason is true.
Assertion
We have,
A
=
15
∘
,
B
=
17
∘
,
C
=
13
∘
⇒
A
+
B
+
C
=
45
∘
⇒
2
A
+
2
B
+
2
C
=
90
∘
∴
P
2
=
2
A
,
Q
2
=
2
B
,
R
2
=
2
C
∴
tan
2
A
tan
2
B
+
tan
2
B
tan
2
C
+
tan
2
C
tan
2
A
=
1
⇒
1
cot
2
A
cot
2
B
+
1
cot
2
B
cot
2
C
+
1
cot
2
C
cot
2
A
=
1
⇒
cot
2
C
+
cot
2
A
+
cot
2
B
cot
2
A
cot
2
B
cot
2
C
=
1
⇒
cot
2
A
+
cot
2
B
+
cot
2
C
=
cot
2
A
cot
2
B
cot
2
C
∴
Assertion is true.
© examsnet.com
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