Verify that each equation is an identity 1 tan theta cot th

Verify that each equation is an identity (1) tan theta + cot theta = sec theta csc theta (2) tan x/2 = csc x - cot x (3) sin t/1 + cos t = 1- cos t/sin t (4) sin 2 theta = 2 tan theta/1+ tan^2 theta (5) cot theta - tan theta = 2 cos^2 theta-1/sin theta cos theta (6) sin theta - tan s/cos s + sin s = cos s - sin s/sin s cos s

Solution

1. tan theta cot theta= (sin theta/cos theta)*(cos thet/sin theta)=1

and csc theta sec theta=1/sintheta cos theta

So its not an identity .

2. tan(x/2)

csc x - cot x = (1-cos x)/ sin x = tan(x/2)

So its an identity