cot x+ tan x = 2 cosec x

Question

trignometry proving

Answer 1

cotx + tanx = cosx/sinx + sinx/cosx

 

                 = (cos²x + sin²x)/(sinxcosx) 

 

                 = 1/(sinxcosx)

 

                 = 2/(2sinxcosx)

 

                 = 2/sin(2x) 

 

                 = 2csc(2x)

 

Note:  the equation that was given is not an identity.  For example,               when x = π/4, cotx+tanx = 2 but 2cscx = 2√2.