" 5.(i) "cot^(2)theta-(1)/(sin^(2)theta)=-1

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

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

Prove: (v) cot^2 theta-(1)/ (sin^2 theta) = -1

(1+(1)/(tan^(2)theta))(1+(1)/(cot^(2)theta))=(1)/(sin^(2)theta-sin^(4)theta)

Prove each of the following identities : (1+ tan^(2) theta)(1+ cot^(2) theta)=(1)/((sin^(2) theta- sin^(4) theta))

Prove that : (i) (1)/(1+tan^(2)theta)+(1)/(1+cot^(2)theta)=1 (ii) sin^(2)theta+(1)/(1+tan^(2)theta)=1

Prove that : (i) (1)/(1+tan^(2)theta)+(1)/(1+cot^(2)theta)=1 (ii) sin^(2)theta+(1)/(1+tan^(2)theta)=1

If cot theta=(1)/(sqrt(3)), show that (1-cos^(2)theta)/(2-sin^(2)theta)=(3)/(5)

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

The numerical value of (1)/(1+cot^(2)theta)+(3)/(1+tan^(2)theta)+2 sin^(2)theta will be