Show that the range of a projectile for two angles `alpha` and `beta` is the same where `alpha+beta=90^@`.

Show that there are two angles of projections for a projectile to have same horizontal range.

The point of intersection of lines is (alpha, beta) , then the equation whose roots are alpha, beta , is

A line makes angles alpha,beta and gamma with the coordinate axes. If alpha+beta=90^0, then find gamma .

If alpha and beta satisfying 2 sec2 alpha = tan beta + cot beta , then alpha+beta =

From the top of a tower, the angles of depression of two objects on the same side of the tower are found to be alpha and beta (alpha >beta) . If the distance between the objects is 'p' metres, show that the height 'h' of the tower is given by h=frac(p tan alpha tan beta)(tan alpha-tan beta) also determine the height of the tower, if p=50 m , alpha=60^@, beta=30^@

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

The lengths of the sides of a triangle are alpha-beta, alpha+beta and sqrt(3alpha^2+beta^2), (alpha>beta>0) . Its largest angle is