given
then evalute 1.
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If cotθ=
8
7
evaluate :
(i)
(1+cosθ)(1−cosθ)
(1+sinθ)(1−sinθ)
(ii) cot
2
θ
Medium
Solution
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cotθ=
8
7
BC
AB
=
8
7
∴AB=7,BC=8
In ⊥ΔABC,∠B=90
0
∴AC
2
=AB
2
+BC
2
=(7)
2
+(8)
2
=49+64
AC
2
=113
∴AC=
113
sinθ=
AC
BC
=
113
8
cosθ=
AC
AB
=
113
7
(i)
(1+cosθ)(1−cosθ)
(1+sinθ)(1−sinθ)
=
(1+
113
7
)(1−
113
7
)
(1+
113
8
)(1−
113
8
)
=
(1)
2
−(
113
7
)
2
(1)
2
−(
113
8
)
2
=
1−
113
49
1−
113
64
=
64
49
(ii) cotθ=
8
7
∴cot
2
θ=(
8
7
)
2
=
64
49
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