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 _________

The minimum value of the expression sin alpha + sin beta+ sin gamma , where alpha,beta,gamma are real numbers satisfying alpha+beta+gamma=pi is

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

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

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

alphaa n dbeta are the positive acute angles and satisfying equation 5sin2beta=3sin2alpha and tanbeta=3tanalpha simultaneously. Then the value of tanalpha+tanbeta is _________

Let alpha , beta be two real numbers satisfying the following relations alpha^(2)+beta^(2)=5 , 3(alpha^(5)+beta^(5))=11(alpha^(3)+beta^(3)) Possible value of alpha + beta is

The value of theta lying between theta=0a n dtheta=pi/2 and satisfying the equation |1+sin^2thetacos^2theta4sin4thetasin^2theta1+cos^2theta4sin4thetasin^2thetacos^2theta1+4sin4theta|=0a r e (7pi)/(24) (b) (5pi)/(24) (c) (11pi)/(24) (d) pi/(24)

alpha, beta, gamma are real number satisfying alpha+beta+gamma=pi . The minimum value of the given expression sin alpha+sin beta+sin gamma is

Q. Let p and q real number such that p!= 0 , p^2!=q and p^2!=-q . if alpha and beta are non-zero complex number satisfying alpha+beta=-p and alpha^3+beta^3=q , then a quadratic equation having alpha/beta and beta/alpha as its roots is