(cos theta)/(1-tan theta)+(sin theta)/(1-cot theta)=

Consider the following statements : 1. If 45^(@) lt theta lt 60^(@) , then sec^(2) theta + cosec^(2) theta = alpha^(2) for some real number alpha gt 1 . 2. If 0^(@) lt theta lt 45^(@) , then (1 + cos theta)/(1- cos theta) = x^(2) for some real number x gt 2 . 3. If 0^(@) lt theta lt 45^(@) , then (cos theta)/(1- tan theta) + (sin theta)/(1 - cot theta) ge 2 . What is the number of true statements ?

Prove that: ((tan theta)/(1-tan theta))-((cot theta)/(1-cot theta))=(cos theta+sin theta)/(cos theta-sin theta)

(sin theta)/(1-cot theta)+(cos theta)/(1-tan theta)=(a)theta(b)1(c)cos theta-sin theta(d)cos theta+sin theta

Show that (sin^2 theta)/(1-cot theta)+(cos^2 theta)/(1-tan theta )=1+sin theta cos theta

(sin theta)/(1-cos theta)+(tan theta)/(1+cos theta)=sec theta cos ec theta-cot theta

(sin theta)/(1-cot theta)+(cos theta)/(1-tan theta) is equal to (a) 0 (b) 1(c)sin theta+cos theta(d)sin theta-cos theta

Prove the following identities: (sin theta)/(1-cos theta)+(tan theta)/(1+cos theta)=sec theta cos ect+cot theta

(tan A) / (1-cot A) + (cot A) / (1-tan A) = 1 + tan A + cot A = 1 + sec A cos ecA (1 + cos theta + sin theta) / (1 + cos theta-sin theta) = (1 + sin theta) / (cos theta)

(tan theta)/(1-cot theta)+(cot theta)/(1-tan theta)=1+sec theta*cos ec theta