simplify
`(1-tan^2theta)/(1-Tan^2theta)`

(1+tan^2theta) sin^2theta

Simplify: (1+tan^(2)theta)(1-sintheta)(1+sintheta)

simplify (1+tan^(2)theta)+(1+(1)/(tan^(2)theta))

Prove that: tan4theta=(4t a ntheta(1-tan^2theta))/(1-6tan^2theta+tan^4theta)

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

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

(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

Prove the following identity: (tan^3theta)/(1+tan^2theta)+(cot^3theta)/(1+cot^2theta)=(1-2sin^2thetacos^2theta)/(sintheta\ costheta)

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

If tan theta+tan(60^(@)+theta)+tan(120^(@)+theta)=3, Prove that: (3tantheta-tan^(3)theta)/(1-3tan^(2)theta)=1