If the distances of the vertices of a triangle =ABC from the points of contacts of the incercle with sides are `alpha,betaa n dgamma` then prove that `r^2=(alphabetagamma)/(alpha+beta+gamma)`

If alpha,beta,gamma, in (0,pi/2) , then prove that (s i(alpha+beta+gamma))/(sinalpha+sinbeta+singamma)<1

Given alpha+beta-gamma=pi, prove that sin^2alpha+sin^2beta-sin^2gamma=2sinalphasinbetacosgammadot

If the distance of the point (alpha,2) from its chord of contact w.r.t. the parabola y^2=4x is 4, then find the value of alphadot

If alpha,betaa n dgamma are the roots of x^3+8=0 then find the equation whose roots are alpha^2,beta^2a n dgamma^2 .

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 line makes angles alpha,betaa n dgamma with the coordinate axes. If alpha+beta=90^0, then find gammadot

The lengths of the tangents drawn from the vertices A, B and C to the incicle of DeltaABC are 5, 3 and 2, respectively. If the lengths of the parts of tangents within the triangle which are drawn parallel to the sides BC, CA and AB of the triangle to the incircle are alpha, beta and gamm , respectively, then the value of [alpha + beta + gamma] (where [.] respresents the greatest integer functin) is _____

A tower AB leans towards west making an angle alpha with the vertical . The anlgular elevation of B , the topmost point of the tower is beta as obsreved from a point C due east of A at distance d from A.If the angular elevation of B from a pont D at a distance 2d due east of C is gamma , then prove that 2 tan alpha = cot gamma -cot beta

If alpha+beta=pi/2a n dbeta+gamma=alpha, then tanalpha equals

If alpha,beta are roots of x^2+p x+1=0a n dgamma,delta are the roots of x^2+q x+1=0 , then prove that q^2-p^2=(alpha-gamma)(beta-gamma)(alpha+delta)(beta+delta) .