Suppose `alpha,betaa n dtheta` are angles satisfying `0

Suppose alpha,beta,gammaa n ddelta are the interior angles of regular pentagon, hexagon, decagon, and dodecagon, respectively, then the value of |cosalphasecbetacosgammacos e cdelta| is _________

if alpha,beta,gamma are non-real numbers satisfying x^3-1=0, then the value of |[lambda+1,alpha,beta],[alpha,lambda+beta,1],[beta,1,lambda+1]|

If hat a , hat b ,a n d hat c are three unit vectors, such that hat a+ hat b+ hat c is also a unit vector and theta_1,theta_2a n dtheta_3 are angles between the vectors hat a , hat b ; hat b , hat ca n d hat c , hat a respectively, then among theta_1,theta_2,a n dtheta_3dot a. all are acute angles b. all are right angles c. at least one is obtuse angle d. none of these

If the angles alpha, beta, gamma of a triangle satisfy the relation, sin((alpha-beta)/(2)) + sin ((alpha -gamma)/(2)) + sin((3alpha)/(2)) = (3)/(2) , then The measure of the smallest angle of the triangle is

If the angles alpha, beta, gamma of a triangle satisfy the relation, sin((alpha-beta)/(2)) + sin ((alpha -gamma)/(2)) + sin((3alpha)/(2)) = (3)/(2) , then Triangle is

vec u , vec v and vec w are three non-coplanar unit vecrtors and alpha,beta and gamma are the angles between vec u and vec v , vec v and vec w ,a n d vec w and vec u , respectively, and vec x , vec y and vec z are unit vectors along the bisectors of the angles alpha,betaa n dgamma , respectively. Prove that [ vecx xx vec y vec yxx vec z vec zxx vec x]=1/(16)[ vec u vec v vec w]^2sec^2(alpha/2)sec^2(beta/2)sec^2(gamma/2) .

If [alphabetagamma-alpha] is to be square root of two-rowed unit matrix, then alpha,betaa n dgamma should satisfy the relation. 1-alpha^2+betagamma=0 b. alpha^2+betagamma=0 c. 1+alpha^2+betagamma=0 d. 1-alpha^2-betagamma=0

A right angle is divided into three positive parts alpha,betaa n dgammadot Prove that for all possible divisions t a nalpha+tanbeta+tangamma>1+tanalphatanbetatangammadot

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

The number of value of alpha in the interval [-pi,0] satisfying sin alpha +int_(alpha )^(2alpha) cos 2 x dx =0 , then