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Answer:
cosecθ+cotθ
=
49
81
⇒49cosecθ+49cotθ=81cosecθ−81cotθ
⇒49cotθ+81cotθ=81cosecθ−49cosecθ
⇒130cotθ=32cosecθ
⇒130
sinθ
cosθ
=32
sinθ
1
⇒65cosθ=16
⇒cosθ=
65
16
PM
2
=OP
2
−OM
2
=65
2
−16
2
⇒PM
2
=(65+16)(65−16)=(81)(49)
⇒PM=
81×49
=9×7=63
cosθ=
OP
OM
=
65
16
,sinθ=
OP
PM
=
65
63
Required expression =
cosθ−sinθ
cosθ+sinθ
=
65
63
−
65
16
65
16
+
65
63
=
65
79
×
47
65
=
47
79
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