`(1+tanalphatanbeta)^2+(tanalpha-tanbeta)^2=`

Prove the following identity: (1+t a nalphat a nbeta)^2+(tanalpha-t a nbeta)^2=sec^2alphasec^2beta

A tree standing on horizontal plane is leaning towards east. At two points situated at distances a and b exactly due west on it, angles of elevation of the top are respectively alpha and beta . Prove that height of the top from the ground is ((b-a).tanalpha.tanbeta)/(tanalpha-tanbeta)

If tanalpha=(1-cosbeta)/(sinbeta),t h e n (a) tan3alpha=tan2beta (b) tan2alpha=tanbeta (c) tan2beta=tanalpha (d) none of these

From an aeroplane vertically above a straight horizontal road, the angles of depression of two consecutive mile stones on opposite sides of the aeroplane are observed to be alphaa n dbeta . Show that the height in miles of aeroplane above the road is give by (tanalphatanbeta)/(tanalpha+tanbeta)

From the top of a light house, the angles of depression of two ships on the opposite sides of its are observed to be alphaa n dbeta . If the height of the light house be h metres and the line joining the ships passes through the foot of the light house, show that the distance between the ship is h(tanalpha+tanbeta)/(tanalphat a nbeta)

If tan(alpha-beta)=(sin2beta,)/(3-cos2beta) then (a) tanalpha=2tanbeta (b) tanbeta=2tanalpha (c) 2tanalpha=3tanbeta (d) 3tanalpha=2tanbeta

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

Let alpha,betaa n dgamma be some angles in the first quadrant satisfying tan(alpha+beta)=(15)/8a n dcos e cgamma=(17)/8, then which of the following hold(s) good? (a) alpha+beta+gamma=pi (b) cotalpha+cotbeta+cotgamma=cotalphacotbetacotgamma (c) tanalpha+tanbeta+tangamma=tanalphatanbetatangamma (d) tanalphatanbeta+tanbetatangamma+tangammatanalpha=1

If acos2theta+bsin2theta= c, alpha and beta as its roots , then prove that tanalpha+t a nbeta=(2 b)/(a+c) , tanalpha*t a nbeta=(c-a)/(c+a) , tan(alpha+beta)=b/a

If tanalpha+tanbeta+tangamma=tanalphatanbetatangamma,then