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Byju's Answer
Standard XII
Mathematics
Tangent, Cotangent, Secant, Cosecant in Terms of Sine and Cosine
A-sin A A-cos...
Question
(
csc
A
−
sin
A
)
(
sec
A
−
cos
A
)
=
1
tan
A
+
cot
A
Open in App
Solution
L.H.S
(
c
o
s
e
c
A
−
sin
A
)
(
sec
A
−
cos
A
)
=
(
1
sin
A
−
sin
A
)
(
1
cos
A
−
cos
A
)
=
(
1
−
sin
2
A
sin
A
)
(
1
−
cos
2
A
cos
A
)
cos
2
A
⋅
sin
2
A
sin
A
cos
A
=
sin
A
cos
A
R.H.S.
=
1
tan
A
+
cot
A
=
1
sin
A
cos
A
+
cos
A
sin
A
=
1
sin
2
A
+
cos
2
A
sin
A
cos
A
=
sin
A
cos
A
Thus, L.H.S
=
R.H.S.
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2
Similar questions
Q.
(
cosec
A
−
sin
A
)
(
sec
A
−
cos
A
)
=
1
tan
A
+
cot
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Q.
(
c
o
sec
A
−
sin
A
)
(
sec
A
−
cos
A
)
=
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+
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Q.
Solve:
(
csc
A
−
sin
A
)
(
sec
A
−
cos
A
)
=
1
tan
A
+
cot
A
Q.
Prove:
(
cosec
A
−
sin
A
)
(
sec
A
−
cos
A
)
=
1
tan
A
+
cot
A
Q.
Prove that :
(
csc
A
−
sin
A
)
(
sec
A
−
cos
A
)
=
1
tan
A
+
cot
A
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Tangent, Cotangent, Secant, Cosecant in Terms of Sine and Cosine
Standard XII Mathematics
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