sin^2 A + sin^2 B + sin^2 C
Answers
Answer:
sin^2A+SIN^2B+SIN^2C
SIN^2(A+B+C)
please mark it as a brainliest answer
Answer:
2
Step-by-step explanation:
sin
2
A
+
sin
2
B
+
sin
2
C
=
2
⇒
1
−
sin
2
A
+
1
−
sin
2
B
−
sin
2
C
=
0
⇒
cos
2
A
+
cos
2
B
−
sin
2
C
=
0
⇒
2
cos
2
A
+
2
cos
2
B
−
2
sin
2
C
=
0
⇒
1
+
cos
2
A
+
1
+
cos
2
B
−
2
(
1
−
cos
2
C
)
=
0
⇒
1
+
cos
2
A
+
1
+
cos
2
B
−
2
+
2
cos
2
C
=
0
⇒
cos
2
A
+
cos
2
B
+
2
cos
2
C
=
0
⇒
2
cos
(
A
+
B
)
cos
(
A
−
B
)
+
2
cos
2
C
=
0
⇒
cos
(
π
−
C
)
cos
(
A
−
B
)
+
cos
2
C
=
0
⇒
−
cos
C
cos
(
A
−
B
)
+
cos
2
C
=
0
⇒
cos
C
cos
(
A
−
B
)
−
cos
2
C
=
0
⇒
cos
C
cos
(
A
−
B
)
−
cos
C
⋅
cos
(
π
−
(
A
+
B
)
)
=
0
⇒
cos
C
[
cos
(
A
−
B
)
+
cos
(
A
+
B
)
]
=
0
⇒
cos
C
⋅
2
cos
A
cos
B
=
0
So any of
A
,
B
and
C
must be
90
∘
If
A
=
90
∘
then
sin
2
A
=
1
And then
B
+
C
=
90
∘
So
sin
2
B
+
sin
2
C
=
sin
2
(
π
2
−
C
)
+
sin
2
C
=
cos
2
C
+
sin
2
C
=
1
Hence
sin
2
A
+
sin
2
B
+
sin
2
C
=
2
is satisfied for any right angled triangle.