Find the distance between the following pairs of points. i) (4,5),(,5,4) ii) (-3,1), (3,2) iii) `(a cos alpha, asin alpha), (a cos beta, a sin beta)`

If tan (alpha-beta)=(sin 2beta)/(3-cos 2beta) , then

cos alpha sin (beta-gamma) + cos beta sin (gamma-alpha) + cos gamma sin (alpha-beta)=

Evaluate : |{:( 0, sin alpha , - cos alpha ), ( - sin alpha , 0 , sin beta) , (cos alpha , -sin beta , 0):}|

If sin beta is the GM between sin alpha and cos alpha, then cos 2beta=

Express the following in a + ib form: ((cos alpha + i sin alpha)^(4))/((sin beta + i cos beta)^(5))

If alpha, beta and gamma the roots of the equation x^(3) + 3x^(2) - 4x - 2 = 0. then find the values of the following expressions: (i) alpha ^(2) + beta^(2) + gamma^(2) (ii) alpha ^(3) + beta^(3) + gamma^(3) (iii) (1)/(alpha)+(1)/(beta)+(1)/(gamma)

Prove that (sin alpha cos beta + cos alpha sin beta) ^(2) + (cos alpha coa beta - sin alpha sin beta) ^(2) =1.

If 2 tan (alpha/2)=tan (beta/2), prove that cos alpha=(3+5 cos beta)/(5+3 cos beta).

If sin alpha = 3/5, find value of (i) sin 3 alpha , (ii) cos 3 alpha (iii) tan 3 alpha.

cos 2 alpha =(3 cos 2 beta -1)/( 3-cos 2 beta), then tan alpha=