" 4.(i) "(1+cos theta)(1-cos theta)(1+cot^(2)theta)=1

Prove each of the following identities : (i) (1+ cos theta)(1- cos theta)(1+ cot^(2) theta)=1 (ii) "cosec" theta (1+ cos theta)("cosec" theta - cot theta)=1

(1 - cos^(2)theta)cot^(2)theta

(1 - cos^(2)theta)cot^(2)theta

cos^(2)theta+1/(1+cot^(2)theta)=1

Given cot theta =(7)/(8) , then evaluate (i) ((1+sin theta )( 1-sin theta ))/( (1+cos theta )(1-cos theta )) " "(ii) cot^2 theta

(sin^(3) theta-cos^(3) theta)/(sin theta - cos theta)- (cos theta)/sqrt(1+ cot^(2) theta)-2 tan theta cot theta=-1 if

(sin ^(3) theta - cos^(3) theta)/(sin theta - cos theta) - (cos theta)/(sqrt(1 + cot^(2)theta))-2 tan theta cot theta = - 1 , if

(sin^(3) theta-cos^(3) theta)/(sin theta - cos theta)- (cos theta)/sqrt(1+ cot^(2) theta)-2 tan theta cot theta=-1 if

(sin^(3) theta-cos^(3) theta)/(sin theta - cos theta)- (cos theta)/sqrt(1+ cot^(2) theta)-2 tan theta cot theta=-1 if

csc theta(1+cos theta)(csc theta-cot theta)=1