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Byju's Answer
Standard X
Mathematics
Range of Trigonometric Ratios from 0 to 90 Degrees
If sinθ+cosθ=...
Question
If (sin θ + cos θ) =
3
, then (tan θ + cot θ) = ?
(a)
1
3
(b)
1
2
(c) 1
(d)
3
2
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Solution
(c) 1
(
sin
θ
+
cos
θ
)
=
3
=>
(
sin
θ
+
cos
θ
)
2
=
3
[
Squaring both sides
]
=>sin
2
θ
+
cos
2
θ
+
2
sin
θ
cos
θ
=
3
=>1+
2
sin
θ
cos
θ
=
3
=>
2
sin
θ
cos
θ
=
2
=>sin
θ
cos
θ
=
1
∴
sin
θ
cos
θ
=
sin
2
θ
+
cos
2
θ
=>
sin
2
θ
+
cos
2
θ
sin
θ
cos
θ
=
1
=>
sin
θ
cos
θ
+
cos
θ
sin
θ
=
1
=>tan
θ
+
cot
θ
=
1
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