trigonometry....help plzz

9

answer is 9.......how did u get it??cud u plzz help?

Well 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

hm..got my mistake.,..thanx..

See , its similar to saying that : when x+y=k , xy has maximum value when x=y=k/2..

yes 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