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Byju's Answer
Standard X
Mathematics
Value of Standard Angle(30,60,90)
Prove the fol...
Question
Prove the following :
(viii)
s
e
c
2
θ
+
cos
e
c
2
θ
=
tan
θ
+
c
o
t
θ
Open in App
Solution
LHS
=
s
e
c
2
θ
+
cos
e
c
2
θ
=
1
+
tan
2
θ
+
1
+
c
o
t
2
θ
(
sin
c
e
,
1
+
tan
2
θ
=
s
e
c
2
θ
,
1
+
c
o
t
2
θ
=
cos
e
c
2
θ
)
=
tan
2
θ
+
c
o
t
2
θ
+
2
=
tan
2
θ
+
c
o
t
2
θ
+
2
tan
θ
.
c
o
t
θ
(
∵
tan
θ
.
c
o
t
θ
=
1
)
=
tan
θ
+
c
o
t
θ
2
=
tan
θ
+
c
o
t
θ
=
RHS
Hence
,
proved
.
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Similar questions
Q.
Prove :
√
s
e
c
2
θ
+
c
o
s
e
c
2
θ
=
tan
θ
+
cot
θ
Q.
If θ is an acute angel such that
s
e
c
2
θ
=
3
,
then find the value of
tan
2
θ
−
c
o
s
e
c
2
θ
tan
2
θ
+
c
o
s
e
c
2
θ
Q.
Prove that:
cosec
2
θ
−
cos
2
θ
cot
2
θ
=
sec
2
θ
−
sin
2
θ
Q.
Prove the following identity.
√
sec
2
θ
+
c
o
s
e
c
2
θ
=
tan
θ
+
cot
θ
Q.
Prove that
(
t
a
n
θ
+
c
o
t
θ
)
2
=
s
e
c
2
θ
+
c
o
s
e
c
2
θ
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