If `(cosecalpha-cotalpha)(cosecbeta-cotbeta)(cosecgamma-cotgamma)`= `(cosecalpha+cotalpha)(cosecbeta+cotbeta)(cosecgamma+cotgamma)`, Prove that each side equals to `+-1`

If (cosecalpha-1)(cosecbeta-1)(cosecgamma-1)=(cosecalpha+1)(cosecbeta+1)(cosecgamma+1), show that each side is equal to pm cotalpha cotbeta cot gamma .

If tanbeta=(2sinalphasingamma)/sin(alpha+gamma) , then cotalpha,cotbeta,cotgamma are in

If cosecalpha+cotalpha=a , prove that , cos alpha =(a^2-1)/(a^2+1) .

If (1+sin alpha)(1+sinbeta)(1+singamma)=(1-sinalpha)(1-sinbeta)(1-singamma) , show that each side is equal to pm cotalpha cotbeta cotgamma .

If tanbeta=2sinalphasingammacos e c(alpha+gamma), then cotalpha,cotbeta,cotgamma are in (a)A.P. (b) G.P. (c) H.P. (d) none of these

If 0ltalphaltpi/2 and sinalpha+cosalpha+tanalpha+cotalpha+secalpha+cosecalpha="7, then prove that sin2alpha is a root of the equation x^2-44x-36=0.

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 the medians of a triangle ABC makes angles alpha , beta , gamma with each other then show that cotalpha+cotbeta+cotgamma+cotA+cotB+cotC=0 .

A tower P Q stands at a point P within the triangular park A B C such that the sides a , ba n dc of the triangle subtend equal angles at P , the foot of the tower. if the tower subtends angles alpha,betaa n dgamma,a tA , Ba n dC respectively, then prove that a^2(cotbeta-cotgamma)+b^2(cotgamma-cotalpha)+a^2(cotalpha-cotbeta)=0

A man observes when he has climbed up 1/3 of the length of an inclined ladder, placed against a wall, the angular depression of an object on the floor is alphadot When he climbs the ladder completely, the angleof depression is beta . If the inclination of the ladder to the floor is theta, then prove that cottheta=(3cotbeta-cotalpha)/2