219
Sinθ+Cosθ=1
then the minimun value of
(1+Cosecθ) (1+Secθ) is .................
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8 Answers
21Well this is my shortcut technique....
it will be a min value when Sinθ=Cosθ
Sinθ+Cosθ=1
SO Sinθ=Cosθ=1/2
Now
(1+ cosec θ)(1 +secθ)
=(1+1sin θ ) (1+1cos θ)
=9 (putting Sinθ=Cosθ=1/2 )
which is the minimum value
Done
1See , its similar to saying that : when x+y=k , xy has maximum value when x=y=k/2..
21yes it will be min when sin θ=cosθ
use differentiation....
Let y=sinθ+cosθ
dydx= cosθ - sinθ
it will be min. when dydx=0
cosθ - sinθ =0
cosθ = sinθ
Proved