Question

The value of tan theta in terms of cosec theta

Answer 1

tanx = sinx/cosc
= sinx/√(1 - sin^2 x)
= (1/cscx)/√(1 - 1/csc^2)
= 1/(cscx√(1 - 1/csc^2) )

replace x with theta

Answer 2

cot^2x + 1 = csc^2x
cotx = 1/tanx
1/tan^2x + 1 = csc^2x
1/tan^2x = csc^2x - 1
tan^2x = 1/(csc^2x - 1)
tanx = √(1/(csc^2x-1))