Question

Show that 1/ 1 + sin (90 -θ) + 1/ 1 - sin (90 -θ) = 2cosec 2 θ

Answer 1

I am using thrita as x
we should first know that sin(90-x)= cosx

now
1/1+sin(90-x) + 1/1-sin(90-x) = 2cosec^2x is to be proved.

Lhs--> 1/1+sin(90-x) + 1/1-sin(90-x)
{using sin(90-x)=cosx}
=1/1+cosx + 1/1-cosx
{taking LCM}
=(1-cosx+1+cosx)÷((1+cosx)(1-cosx))
= 2/(1-cos^2x). {using cos^2x + sin^2x=1}
=2/sin^2x
=2cosec^2x

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