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Byju's Answer
Standard X
Mathematics
Visualisation of Trigonometric Ratios Using a Unit Circle
In Fig. 3, fr...
Question
In Fig. 3, from an external point P, two tangents PT and PS are drawn to a circle with centre O and radius r. If
O
P
=
2
r
, show that
∠
O
T
S
=
∠
O
S
T
=
30
∘
.
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Solution
We have,
O
P
=
2
r
Let
∠
T
O
P
=
θ
In
Δ
O
T
P
,
c
o
s
θ
=
O
T
O
P
=
r
2
r
=
1
2
∵
θ
=
60
∘
Hence,
∠
T
O
S
=
2
θ
=
2
×
60
∘
=
120
∘
In
Δ
T
O
S
∠
T
O
S
+
∠
O
T
S
+
∠
O
S
T
=
180
∘
120
∘
+
2
∠
O
T
S
=
180
∘
(
∵
∠
O
T
S
=
∠
O
S
T
)
2
∠
O
T
S
=
180
∘
−
120
∘
∠
O
T
S
=
30
∘
Hence,
∠
O
T
S
=
∠
O
S
T
=
30
∘
Hence Proved.
Suggest Corrections
75
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