`cos^(2)theta(1+tan^(2)theta)=1`

Prove that: cos^2theta(1+tan^2theta)=1 .

tan theta+(1)/(tan theta)=2 then prove that tan^(2)theta+(1)/(tan^(2)theta)=2

If theta=30o, verify that: ( i )cos2 theta=(1-tan^(2)theta)/(1+tan^(2)theta)( ii) cos3 theta=4cos^(3)theta-3cos theta

Prove that : (1 - tan^(2) theta)/(1 + tan^(2) theta) = cos^(2) theta - sin^(2) theta

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

Show that (cos^(2)theta - sin^(2)theta)=(2tan theta)/((1- tan^(2)theta)) is not an identity .

If 3cot theta=4 then show that (1-tan^(2)theta)/(1+tan^(2)theta)=(cos^(2)theta-sin^(2)theta)

By using above basic addition/ subtraction formulae, prove that (i) tan (A+B)=(tan A+tan B)/(1-tan A tan B) , (ii) tan (A-B)=(tan A-tanB)/(1+tan A tan B) (iii) sin2theta=2sintheta costheta , (iv) cos2theta=cos^(2)theta=1-2sin^(2)theta=2cos^(2)theta-1 (v) tan 2theta=(2 tan theta)/(1-tan^(2) theta)

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