if tan A= 1/√5,
Find (cosec A - sec A)/(cosec A + sec A).
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Step-by-step explanation:
Solution:-
tanA=
5
1
{Given}
∴sinA=
1+tan
2
A
tanA
=
1+(
5
1
)
2
(
5
1
)
=
6
1
⇒cscA=
sinA
1
=
(
6
1
)
1
=
6
⇒csc
2
A=(
6
)
2
=6
cosA=
1+tan
2
A
1
=
1+(
5
1
)
2
1
=
6
5
⇒secA=
cosA
1
=
(
6
5
)
1
=
5
6
⇒sec
2
A=(
5
6
)
2
=
5
6
∴
csc
2
A+sec
2
A
csc
2
A−sec
2
A
=
6+
5
6
6−
5
6
=
3
2
∴
csc
2
A+sec
2
A
csc
2
A−sec
2
A
=
3
2
=
m
1
⇒m=
2
3
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