Prove the following trigonometric identities sec thetatan th

Prove the following trigonometric identities. sec theta/tan theta = csc theta (sec x + tan x)(1 - sin x/cos x) = 1

Solution

sec theta/tan theta=csc theta

sec theta=1/cos theta (reciprocal rule)

and tan theta=sin theta/cos theta    (quotient rule)

1/cos theta/sin theta/cos theta           (substitution postulate)

1/sin theta = csc theta       (reciprocal rule)