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Byju's Answer
Standard XII
Mathematics
Trigonometric Ratios of Compound Angles
Prove that -1...
Question
Prove that -
1 +
s
i
n
2
θ
+
s
i
n
2
ϕ
> sin
θ
+ sin
ϕ
+ sin
θ
sin
ϕ
.
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Solution
Apply
a
2
+
b
2
+
c
2
>
a
b
+
b
c
+
c
a
∵
a
2
+
b
2
>
2
a
b
,
b
2
+
c
2
>
2
b
c
,
c
2
+
a
2
>
2
c
a
add etc.
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0
Similar questions
Q.
Prove that :
cos
2
θ
cos
2
ϕ
+
sin
2
(
θ
−
ϕ
)
−
sin
2
(
θ
+
ϕ
)
=
cos
2
(
θ
+
ϕ
)
Q.
Prove that the product of matrices
[
cos
2
θ
cos
θ
sin
θ
cos
θ
sin
θ
sin
2
θ
]
and
[
cos
2
ϕ
cos
ϕ
sin
ϕ
cos
ϕ
sin
ϕ
sin
2
ϕ
]
is the null matrix, when
θ
and
ϕ
differ by an odd multiple of
π
2
.
Q.
If
sin
θ
+
sin
ϕ
=
a
and
cos
θ
+
cos
ϕ
=
b
,
(
a
≠
b
,
a
≠
0
,
b
≠
0
)
then -
Q.
If
θ
−
ϕ
=
π
/
2
then show that
[
cos
2
θ
cos
θ
sin
θ
cos
θ
sin
θ
sin
2
θ
]
[
cos
2
ϕ
cos
ϕ
sin
ϕ
cos
ϕ
sin
ϕ
sin
ϕ
]
= 0$
Q.
The angle of elevation of a certain peak when observed, from each end of a horizontal base line of length 2a is found to be
θ
. When observed from the mid-point of the base the angle of elevation is
ϕ
. Then the height of the peak is
a
s
i
n
θ
s
i
n
ϕ
√
(
s
i
n
(
ϕ
+
θ
)
s
i
n
(
ϕ
−
θ
)
)
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