∫π/6π/2csctcott dt =1
The Fundamental Theorem of Calculus: Suppose f is continuous on [a, b], then
∫abfxdx=Fb-F(a), where F is antiderivative of f, that is F'=f.
By using the antiderivative of the function,
Applying the Fundamental Theorem of Calculus,
After substituting values of sinπ2 and sinπ6,
Therefore,∫π/6π/2csctcott dt =1