Suppose `alpha,beta a n d theta` are angles satisfying `0 < alpha < theta < beta < pi/2 dot` Then prove that `(sin alpha-sin beta)/(cos beta-cos alpha)=-cot theta`

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 _________

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

The number of ordered pairs (alpha,beta) , where alpha,betain(-pi,pi) satisfying cos(alpha-beta)=1 andcos(alpha-beta)=1 and cos(alpha+beta)=1/e 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 [[alpha, beta], [gamma, -alpha]] is to be square root of two-rowed unit matrix, then alpha,beta and gamma should satisfy the relation. a. 1-alpha^2+betagamma=0 b. alpha^2+betagamma=0 c. 1+alpha^2+betagamma=0 d. 1-alpha^2-betagamma=0

Three angles of a triangle are alpha-beta,alpha,alpha+beta . If the greatest angle is 2 times of the smallest angle then find the general angle in circular measure.

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)) Quadratic equation having roots alpha and beta is

If sin alpha = 1/sqrt10, cos beta = 2/sqrt5 "and" alpha, beta are positive acute angles, then find the value of (alpha + beta)

Find the values of the parameter a such that the rots alpha,beta of the equation 2x^2+6x+a=0 satisfy the inequality alpha//beta+beta//alpha<2.

If alpha,beta,gamma are the angles of a triangle and system of equations cos(alpha-beta)x+cos(beta-gamma)y+cos(gamma-alpha)z=0 cos(alpha+beta)x+cos(beta+gamma)y+cos(gamma+alpha)z=0 sin(alpha+beta)x+sin(beta+gamma)y+sin(gamma+alpha)z=0 has non-trivial solutions, then triangle is necessarily a. equilateral b. isosceles c. right angled "" d. acute angled