Find the distance between each of the following pairs of points :
`(acosalpha, a sin alpha),(acos beta,a sin beta)`, where a is a positive real number.

Find the derivatives of the following : 3 sin x + 2 sin alpha , where alpha is a constant.

Using vectors, prove that sin (alpha+beta)=sin alpha cos beta+ cos alpha sin beta .

Using vectors prove that sin(alpha - beta) = sin alpha cos beta- cos alpha sin beta .

Prove by vectors that : cos (alpha + beta) = cos alpha cos beta- sin alpha sin beta .

Prove by vectors that : cos (alpha - beta) = cos alpha cos beta+ sin alpha sin beta .

If "cot"(alpha+beta=0, then "sin"(alpha+2beta can be

Prove that the area of the parallelogram formed by the lines x cos alpha+y sin alpha=p ,x cos alpha+y sin alpha=q , x cos beta+y sin beta=r and x cos beta+y sin beta=s is ±(p−q)(r−s)cosec(α−β).

The lines x cos alpha + y sin alpha = P_1 and x cos beta + y sin beta = P_2 will be perpendicular, if :

If tan (alpha- beta)= (sin 2 beta)/(5-cos 2 beta) , find tan alpha: tan beta .

If cos alpha+ cos beta + cos gamma = sin alpha+ sin beta +sin gamma= 0 , then :