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Byju's Answer
Standard X
Mathematics
Standard Values of Trigonometric Ratios
i 1+cosθ1-cos...
Question
(i) (1 + cos θ) (1 − cos θ) (1 + cot
2
θ) = 1
(ii) cosec θ (1 + cos θ) (cosec θ − cot θ) = 1
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Solution
(
i
)
LHS=
(
1
+
cos
θ
)
(
1
−
cos
θ
)
(
1
+
cot
2
θ
)
=
(
1
−
cos
2
θ
)
cosec
2
θ
=sin
2
θ
×
cosec
2
θ
=sin
2
θ
×
1
sin
2
θ
=1
=RHS
(
ii
)
LHS=cosec
θ
(
1
+
cos
θ
)
(
cosec
θ
−
cot
θ
)
=
(
cosec
θ
+cosec
θ
×cos
θ
)
(
cosec
θ
−
cot
θ
)
=
(
cosec
θ
+
1
sin
θ
×
cos
θ
)
(
cosec
θ
−
cot
θ
)
=
(
cosec
θ
+cot
θ
)
(
cosec
θ
−
cot
θ
)
=cosec
2
θ
−
cot
2
θ
(
∵
cosec
2
θ
−
cot
2
θ
=
1
)
=1
=RHS
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Similar questions
Q.
If
cot
θ
=
7
8
, evaluate :
(i)
1
+
sin
θ
1
-
sin
θ
1
+
cos
θ
1
-
cos
θ
(ii) cot
2
θ