`(tan^(2)theta-1)/(tan^(4)theta-1) = cos^2 theta`

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

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

If theta=30^@ , verify that: (i) cos2theta=(1-tan^2theta)/(1+tan^2theta) (ii) cos3theta=4cos^3theta-3costheta

If (2tan^(2)theta_(1)tan^(2)theta_(2)tan^(2)theta_(3)+tan^(2)theta_(1)tan^(2)theta_(2)+tan^(2)theta_(2)tan^(2)theta_(3)+tan^(2)theta_(3)tan^(2)theta_(1)=1 then which of the following relations hold good ?

Prove that ("tan"^(2)theta)/(("sec"theta-1)^(2))=(1+"cos"theta)/(1-"cos"theta) .

Prove that (tan^(2)2theta-tan^(2)theta)/(1-tan^(2)2thetatan^(2)theta)=tan 3 theta tan theta .

Prove that (tan^2 (2theta)-tan^2 theta)/(1-tan^2 (2theta) tan^2 theta)=tan (3theta)tan theta

Prove that : (i) 1+(cos^(2)theta)/(sin^(2)theta)-"cosec"^(2)theta=0 (ii) (1+tan^(2)theta)/("cosec"^(2)theta)=tan^(2)theta

If tan^(4)theta +tan^(2) theta = 2 , then the value of cos^(4)theta +cos^(2)theta is-

(i) The points (-1, 0), (4, -2) and (cos 2theta, sin 2 theta) are collinear (ii) The points (-1,0), (4, -2) and ((1-tan^(2)theta)/(1+tan^(2)theta),(2tan theta)/(1+tan^(2)theta)) are collinear