If `secalpha=5/4`, evaluate `(1-tanalpha)/(1+tanalpha)`.

If secalpha=5/4 , verify that (tanalpha)/(1+tan^2alpha)=(sinalpha)/(secalpha)

Find the adjoint of the following matrices: [(cosalpha,sinalpha),(sinalpha,cosalpha)] (ii) [(1,tanalpha//2),(-tanalpha//2, 1)] Verify that (a d j\ A)A=|A|I=A(a d j\ A) for the above matrices.

By geometrical interpretation, prove that tan(alpha+beta)=(tanalpha+tanbeta)/(1-tanalphatanbeta) .

If sin theta=n"sin"(theta+2alpha) , prove that tan(theta+alpha)=(1+n)/(1-n)tanalpha .

In A B C , on the side B C ,D and E are two points such that B D=D E=E Cdot Also /_A D E=/_A E D=alpha, then (a) 3(tanB+tanc)=2tanalpha (b) tanB+tanC=3tanalpha (c) tanA=(6tanalpha)/(9-tan^2alpha) (d) tanA=(6tanalpha)/(tan^2alpha-9)

A vertical tower Stands on a horizontal plane and is surmounted by a vertical flag staff of height h. At a point on the plane, the angles of Elevation of the bottom and the top of the flag staff are alpha and beta respectively Prove that the height of the tower is (htanalpha)/(tanbeta - tanalpha)

A vertical tower stands on a horizontal plane and is surmounted by a vertical flag staff of height h. At a point on the plane, the angles of Elevation of the bottom and the top of the flag staff are alpha and beta respectively. Prove that the height of the tower is (htanalpha)/(tanbeta - tanalpha)

A vertical tower sands on a horizontal plane and is surmounted by a vertical flag staff of height hdot At a point on the plane, the angles of elevation of the bottom and the top of the flagstaff are alpha and beta .Prove that the height of the tower (htanalpha)/(tanbeta-tanalpha)

If tanalpha+cotalpha=2 , then

The set of all possible values of alpha in [-pi,pi] such that sqrt((1-sinalpha)/(1+sinalpha)) is equal to sec alpha-tanalpha, is