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Byju's Answer
Standard XII
Mathematics
Product of Trigonometric Ratios in Terms of Their Sum
sinθ -cosθ +1...
Question
sin
θ
−
cos
θ
+
1
sin
θ
+
cos
θ
−
1
=
1
sec
θ
−
tan
θ
.
Open in App
Solution
L
H
S
=
sin
θ
−
cos
θ
+
1
sin
θ
+
cos
θ
−
1
=
sin
θ
−
cos
θ
+
1
sin
θ
+
cos
θ
−
1
×
sin
θ
+
cos
θ
+
1
sin
θ
+
cos
θ
+
1
=
[
(
sin
θ
+
1
)
−
cos
θ
]
[
(
sin
θ
+
1
)
+
cos
θ
]
(
sin
θ
+
cos
θ
)
2
−
1
=
(
sin
θ
+
1
)
2
−
cos
2
θ
(
sin
θ
+
cos
θ
)
2
−
1
=
1
+
sin
2
θ
+
2
sin
θ
−
cos
2
θ
sin
2
θ
+
2
sin
θ
cos
θ
+
cos
2
θ
−
1
=
2
sin
2
θ
+
2
sin
θ
2
sin
θ
cos
θ
[
∵
sin
2
A
+
cos
2
A
=
1
]
=
2
sin
θ
(
sin
θ
+
1
)
2
sin
θ
cos
θ
=
sin
θ
+
1
cos
θ
=
sin
θ
+
1
cos
θ
×
(
−
sin
θ
+
1
)
(
−
sin
θ
+
2
)
1
−
sin
2
θ
cos
θ
(
1
−
sin
θ
)
cos
2
θ
cos
(
θ
)
(
1
−
sin
θ
)
=
1
1
−
sin
θ
cos
θ
=
sec
θ
−
tan
θ
=
R
H
S
So,
L
H
S
=
R
H
S
Suggest Corrections
0
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If
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−
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