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asecθ+btanθ=1,asecθ−btanθ=5
cosθ
a+bsinθ
=1
a+bsinθ=cosθ.....(i)
cosθ
a−bsinθ
=5
a−bsinθ=5cosθ.......(ii)
addingequation(i)and(ii)
a+bsinθ=cosθ
a−bsinθ=5cosθ
2a=6cosθ
a=3coθ,a
2
=qcos
2
θ
puttingthevalueobtained(ii)
3cosθ−bsinθ=5cosθ
−2cosθ=bsinθ
−2cotθ=b,b
2
=4cot
2
θ
thena
2
(b
2
+4)=9cos
2
θ[4(1+cot
2
θ)]
=36cos
2
θ.cosec
2
θ
=36(
sinθ
cosθ
)
2
=36×cot
2
θ[⋅.⋅cot
2
θ=
4
b
2
]
=
4
36
b
2
9b
2
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