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

An aeroplane is flying above a horizontal plane. The angle of depression of two consecutive mile stones at plane in opposite directions are respectively alpha and beta . Prove that height of the aeroplane is (tanalphatanbeta)/(tanalpha+tanbeta)

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

tan^2 alpha+2tan alpha.tan2beta=tan^2 beta+2tan beta.tan2 alpha, if (A) tan^2 alpha+2tan alpha.tan2beta=0 (B) tan alpha+tan beta=0 (C) tan^2 beta+2tanbeta,tan2 alpha=1 (D) tan alpha=tan beta

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+tanbeta+tangamma=tanalphatanbetatangamma (c)tanalpha+tanbeta+tangamma=tanalphatanbetatangamma (d)tanalphatanbeta+tanbetatangamma+tangammatanalpha=1

If tanalpha+tanbeta+tangamma=tanalphatanbetatangamma,then

If alpha+beta+gamma=2pi, then- a.tanalpha/2+(tan beta)/2+tangamma/2=tanalpha/2tanbeta/2tangamma/2 b. tanalpha/2+tanbeta/2+tan"(beta/2)tangamma/2=tangamma/2tanalpha/2=1 c.tanalpha/2+t a nbeta/2+tangamma/2=tanalpha/2tanbeta/2tangamma/2 d.tan(alpha/2)tan(beta/2) +tan(gamma/2)tan(beta/2) +tan(gamma/2)tan(alpha/2) =0

The angle of elevation of the top of a tower as observed from a point on the ground is a and on moving 'a' metres towards the tower, the angle of elevation is beta . Prove that the height of the tower is (a tanalphatanbeta)/(tanbeta-tanalpha) .

Given that p = tanalpha+tanbeta, andq=cotalpha+cotbeta , then what is ((1)/(p)-(1)/(q)) equal to ?

If (tanalpha+tanbeta)/(cot alpha+cot beta)+{cos(alpha-beta)+1}^(-1)=1, then tan alpha tan beta is equal to

Prove that : cos^(-1)((cosalpha+cosbeta)/(1+cosalphacosbeta))=2\ tan^(-1)(tanalpha/2tanbeta/2)