60. If cosec - cote = mand coser
=m and cosec-oi = 1, prove that mon=1
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Answer:
Let, cosecA+cotA=m
Then
m
2
−1
m
2
+1
=
cosec
2
A+cot
2
A+2cosecA.cotA−1
cosec
2
A+cot
2
A+2cosecA.cotA+1
=
2cot
2
A+2cosecA.cotA
2cosec
2
A+2cosecA.cotA
[Since cosec
2
A−1=cot
2
A and 1+cot
2
A=cosec
2
A]
=
cotA
cosecA
=secA.........(1).
Now
m
2
+1
m
2
−1
=cosA [Using (1)]
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