if sin theta = root 3/2 then cosec theta + cot theta

 if sin theta = root 3/2 then cosec theta + cot theta

Solution:- Given that sinϴ=√3/2

We have to find value of cosecϴ + cotϴ............ (A) 

We know that sinϴ=perpendicular(P)/hypotaneous(H) 

So, perpendicular(P)=√3

hypotaneous(H)=2

Again we know that by Pythagorean theorem, 

Base(b) =√(H^2-p^2) 

So, b=2^2-(√3)^2

b=4-3=1

b=1

(A)⇒ cosecϴ + cotϴ=hypotaneous(H)/perpendicular(P)+Base(b)/perpendicular(P), 

So, cosecϴ + cotϴ

= 2/√3 -1/√3

=2-1/√3

=1/√3 ans...