[" 7) Show that nane of the following is an identity: "],[" () "cos^(2)theta+cos theta=1]

Show that none of the following is an identity: (i) cos^(2) theta + cos theta =1 " " (ii) sin^(2) theta + sin theta =2 " " (iii) tan^(2) theta + sin theta = cos^(2) theta

Prove the following identity : cot^2 theta- cos^2 theta= cot^2 theta cos^2 theta .

Prove the following identity : sin^4 theta+ cos^4 theta= 1-2 sin^2 theta cos^2 theta .

Prove the following identity : sin^6 theta+ cos^6 theta= 1-3 sin^2 theta cos^2 theta .

Prove the following identity : (1-cos theta)/(sin theta)= (sin theta)/(1+cos theta) .

Prove the following identity : (sin theta)/(1-cos theta)= (1+cos theta)/(sin theta) .

Prove the following identity: (1+cot theta-cos ec theta)(1+tan theta+sec theta)=2

Prove the following identities : sec^(2)theta-cos^(2)theta=sin^(2)theta(sec^(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

Prove the following trigonometric identities : (1+cot^(2)theta)(1-cos theta)(1+cos theta)=1( ii) tan^(2)theta-(1)/(cos^(2)theta)=-1