If `tan theta =p/q`, show that :
`(p sin theta-q cos theta)/(p sin theta+q cos theta)= (p^2-q^2)/(p^2+q^2)`.

Find sin 2 theta when sin theta + cos theta= 1 .

Prove that : sin 2 theta= 2sin theta cos theta .

sin^2theta+cos^2theta=1 .

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

Prove that : sin^8 theta- cos^8 theta= (sin^2 theta- cos^2 theta)(1-2 sin^2 theta cos^2 theta) .

If tan theta=12/5 , calculate sin theta , cos theta and verify sin^2theta+cos^2theta .

Prove that sin^4theta-cos^4theta=sin^2theta-cos^2theta .

Prove that : (sin theta)/(1+cos theta) + (1+cos theta)/(sin theta)= 2 cosec theta .

Solve sqrt(3) cos theta-3 sin theta =4 sin 2 theta cos 3 theta .

ABCD is a trapezium such that AB and CD are parallel and BC bot CD . If angleADB = theta, BC = p and CD = q , then AB is equal to (a) ((p^(2)+q^(2))sin theta)/(p cos theta +q sin theta) (b) (p ^(2) + q ^(2)cos theta)/(p cos theta +q sin theta) (c) (p ^(2)+ q^(2))/(p^(2)cos theta +q^(2) sin theta) (d) ((p^(2) +q^(2))sin theta)/((p cos theta + sin theta)^(2))