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Byju's Answer
Standard XII
Mathematics
Tangent, Cotangent, Secant, Cosecant in Terms of Sine and Cosine
Prove that: ...
Question
Prove that:
(
1
+
tan
A
+
cot
A
)
(
sin
A
−
cos
A
)
=
sin
A
tan
A
−
cot
A
cos
A
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Solution
Now,
(
1
+
tan
A
+
cot
A
)
(
sin
A
−
cos
A
)
=
(
sin
A
−
cos
A
)
+
(
tan
A
.
sin
A
−
cos
A
.
tan
A
)
+
(
cot
A
.
sin
A
−
cot
A
cos
A
)
=
(
sin
A
−
cos
A
)
+
(
tan
A
.
sin
A
−
sin
A
)
+
(
cot
A
.
sin
A
−
cot
A
.
cos
A
)
=
(
−
cos
A
)
+
(
tan
A
.
sin
A
)
+
(
cos
A
−
cot
A
.
cos
A
)
=
tan
A
.
sin
A
−
cos
A
.
cot
A
.
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Similar questions
Q.
Prove that
(
1
+
cot
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+
tan
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)
(
sin
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−
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)
=
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−
cot
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cos
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Q.
Prove the following trigonometric identities.
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cosec
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-
cosec
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sec
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tan
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cot
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