If `sin(alpha+beta)sin(alpha-beta)=singamma(2sinbeta+singamma),` where `0 < alpha,beta,gamma < pi,` then the straight line whose equation is `xsinalpha+ysinbeta-singamma=0` passes through point (a) `(1,1)` (b) `(-1,1)` (c) `(1,-1)` (d) none of these

alpha,beta,gammaa n ddelta are angle in I, II, III and iv quadrants, respectively and none of them is an integral multiple of pi/2dot They form an increasing arithmetic progression. Which of the following holds? cos(alpha+delta)>0 cos(alpha+delta)=0 cos(alpha+delta) 0orcos(alpha+delta)<0 Which of the following does not hold? sin(beta+gamma)=sin(alpha+delta) sin(beta-gamma)="sin"(alpha-delta) sin(alpha-beta)="tan"(beta-delta) sin(alpha+gamma)=cos2beta) If alpha+beta+gamma+delta=thetaa n dalpha=70^0, then 400^0

It cos(alpha+beta)=4/5,sin(alpha-beta)=5/(13)a n dalpha,beta lie between 0a n dpi/4 , prove that tan2alpha=(56)/(33)

If cosalpha=1/2(x+1/x)a n dcosbeta=1/2(y+1/y),(x y >0); x , y ,alpha,beta in R then sin(alpha+beta+gamma+singammaAAgamma in R cosalphacosbeta=1AAalpha,beta in R (cosalpha+cosbeta)^2=4AAalpha,beta in R sin(alpha+beta+gamma)=sinalpha+sinbeta+s ingammaAAa , b ,gamma in R

If cosalpha+2cosbeta+3cosgamma=sinalpha+2sinbeta+3singamma=0 , then the value of sin3alpha+8sin3beta+27sin3gamma is a. sin(alpha+beta+gamma) b. 3sin(alpha+beta+gamma) c. 18"sin"(alpha+beta+gamma) d. sin(alpha+2beta+3)

Find the value of x such that ((x+alpha)^2-(x+beta)^2)/(alpha+beta)=(sin (2theta))/(sin^2 theta) , where alpha and beta are the roots of the equation t^2-2t+2=0 .

If (tan(alpha+beta-gamma))/("tan"(alpha-beta+gamma))=(tangamma)/(tanbeta),(beta!=gamma) then sin2alpha+sin2beta+sin2gamma= (a) 0 (b) 1 (c) 2 (d) 1/2

If a =cos alpha - i sin alpha, b= cos beta - i sin beta, c = cos gamma - i sin gamma , then ((a^2c^2 - b^2)/(abc)) is …………..

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

P(cosalpha,sinalpha), Q(cosbeta, sinbeta) , R(cosgamma, singamma) are vertices of triangle whose orthocenter is (0, 0) then the value of cos(alpha-beta) + cos(beta-gamma) + cos(gamma-alpha) is

If cos alpha + cos beta + cos gamma = sin alpha + sin beta + sin gamma = 0 , show that sin 3alpha + sin 3 beta + sin 3gamma = 3 sin (alpha + beta + gamma)