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 a line makes angles alpha,betaa n dgamma with threew-dimensional coordinate axes, respectively, then find the value of cos2alpha+cos2beta+cos2gammadot

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

If alpha,beta,gamma,delta are the roots of the equation x^4-K x^3+K x^2+L x+m=0,w h e r eK ,L ,a n dM are real numbers, then the minimum value of alpha^2+beta^2+gamma^2+delta^2 is a. 0 b. -1 c. 1 d. 2

A line makes angles alpha,beta,gammaa n ddelta with the diagonals of a cube. Show that cos^2alpha+cos^2beta+cos^2gamma+cos^2delta=4//3.

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

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

Suppose alpha,betaa n dtheta are angles satisfying 0

Three parallel chords of a circle have lengths 2,3,4 units and subtend angles alpha,beta,alpha+beta at the centre, respectively (alphaltbetaltpi), then find the value of cosalpha

A circle of area 20 sq. units is centered at the point O. Suppose DeltaABC is inscribed in that circle and has area 8 sq. units. The central angles alpha, beta and gamma are as shown in the figure. The value of (sin alpha+sin beta+sin gamma) is equal to

Computing area with parametrically represented boundaries : If the boundary of a figure is represented by parametric equation, i.e., x=x(t), y=y(t), then the area of the figure is evaluated by one of the three formulas : S=-int_(alpha)^(beta)y(t)x'(t)dt, S=int_(alpha)^(beta)x(t)y'(t)dt, S=(1)/(2)int_(alpha)^(beta)(xy'-yx')dt, Where alpha and beta are the values of the parameter t corresponding respectively to the beginning and the end of the traversal of the curve corresponding to increasing t. The area of the loop described as x=(t)/(3)(6-t),y=(t^(2))/(8)(6-t) is