Find Cot
(TT/4+A)in terms of Cot A.
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We have
1]cosec
2
A−cot
2
A=1
⇒cosec
2
A=1+cot
2
A
⇒(cosecA)
2
=cot
2
A+1
⇒(
sinA
1
)
2
=cot
2
+1
⇒(sinA)
2
=
cot
2
A+1
1
⇒sinA=±
cot
2
A+1
1
We reject the negative value of sinA for acute angle A. Therefore sinA=
cot
2
A+1
1
2]tanA=
cotA
1
3]We have sec
2
A−tan
2
A=1
⇒sec
2
A=1+tan
2
A
⇒sec
2
A=1+
cot
2
A
1
=
cot
2
A
cot
2
A+1
⇒secA=
cotA
cot
2
A+1
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