If `x=a sin alpha+b cos alpha` and `y=a cos alpha-b sin alpha` then remove `alpha`

IF tan alpha = ( sin alpha - cos alpha )/( sin alpha + cos alpha) , then sin alpha + cos alpha is

If x=a ( " cosec " alpha + cot alpha) and y=(b(1- cos alpha))/(sin alpha ) , then

If x sin ^3 alpha + y cos^3 alpha = sin alpha cos alpha and x sin alpha - y cos alpha =0 , then x^2 +y^2 is

|(sin alpha, cos alpha),(cos alpha, -sin alpha)|=

If sin alpha + cos alpha = b, then sin 2 alpha is equal to

Prove that, (cos alpha + sin alpha)/(cos alpha -sin alpha)-(cos alpha - sin alpha)/(cos alpha + sin alpha) = 2 tan 2 alpha

Find the distance between the following pair of points: (a sin alpha,-b cos alpha) and (-a cos alpha,b sin alpha)( ii) (a,0) and (0,b)

( sin 8 alpha * cos alpha - sin 6 alpha * cos 3 alpha )/(cos 2 alpha cos alpha - sin 3 alpha * sin 4alpha ) =

( sin alpha sin 3alpha + sin 3alpha sin 7 alpha + sin 5 alpha sin 15 alpha )/( sin alpha cos 3 alpha + sin 3alpha cos 7 alpha + sin 5 alpha cos 15 alpha ) =