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Byju's Answer
Standard XII
Mathematics
Direction Cosines
If a line mak...
Question
If a line makes angle
(
α
,
β
,
γ
)
with the co-ordinates axes. Prove that
sin
2
α
+
sin
2
β
−
cos
2
γ
=
1
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Solution
l
=
cos
α
m
=
cos
β
n
=
cos
γ
Now
l
2
+
m
2
+
n
2
=
1
cos
2
α
+
cos
2
β
+
cos
2
γ
=
1
1
−
sin
2
α
+
1
−
sin
2
β
+
cos
2
γ
=
1
2
−
sin
2
α
−
sin
2
β
+
cos
2
γ
=
1
sin
2
α
+
sin
2
β
+
1
−
cos
2
γ
−
2
=
0
sin
2
α
+
sin
2
β
−
cos
2
γ
−
1
=
0
sin
2
α
+
sin
2
β
−
cos
2
γ
=
1
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