Relation between `cos theta` and `sin theta`

what is the relation between a cos theta+b sin theta=p and a sin theta-b cos theta=q

The distance between (a cos theta + b sin theta ,0) and (0,a sin theta - bcos theta ) is

If sin theta =a and sin 2 theta = b, find an expression for cos theta in terms of a and b. Hence find a relation between a and b not involving theta.

Find the A.M. between: ( cos theta + sin theta )^(2) and ( cos theta - sin theta)^(2)

Evaluate : sin theta cos theta - (sin theta cos (90^(@) - theta) cos theta)/( sec (90^(@) - theta)) - (cos theta sin (90^(@) - theta) sin theta)/( cosec (90^(@) - theta))

Eliminate theta between the equation : x =a cos theta + b sin theta, y =a sin theta- b cos theta .

(sin theta + cos theta)/(sin theta - cos theta) + (sin theta - cos theta)/(sin theta + cos theta)= ________

(cos theta + sin theta )/( cos theta - sin theta )-(cos theta - sin theta )/( cos theta + sin theta ) =

Eliminate theta between the relations tan theta+sin theta=p and tan theta-sin theta=q

What is the distance between the points A(sin theta-cos theta,0) and B(0,sin theta+cos theta)?