If vector ` vec b=(t a nalpha,-1, 2sqrt(sinalpha//2))a n d vec c=(t a nalpha, t a nalpha, -3/(sqrt(sinalpha//2)))` are orthogonal and vector ` vec a=(1,3,sin2alpha)` makes an obtuse angle with the z-axis, then the value of `alpha` is

If 4nalpha=pi , then the numerical value of tanalpha, tan2alpha,tan3alpha.....tan(2n-1)alpha is equal to

If 4nalpha=pi , then cotalpha cot2alpha cot3alpha.... cot(2n-1)alpha is equal to

If alpha in [pi/2,pi] , then the value of sqrt(1+sin alpha)- sqrt(1-sinalpha) is equal to:

Prove that: t a nalpha+2tan2alpha+4tan4alpha+8cot8alpha=cotalpha

If vec alpha, vec beta, vecgamma be three unit vectors such that |vec alpha+vec beta+vec gamma|=1 and vec alpha is perpendicular to vec beta while vec gamma makes angles theta and phi with vec alpha and vec beta respectively, then the value of cos theta+cos phi is -

The value of the integral int_0^1(dx)/(x^2+2xcosalpha+1) is equal to (a) sinalpha (b) alphasinalpha (c) alpha/(2sinalpha) (d) alpha/2sinalpha

Given three vectors vec a=6 hat i-3 hat j , vec b=2 hat i-6 hat ja n d vec c=-2 hat i+21 hat j such that vecalpha= vec a+ vec b+ vec c Then the resolution of the vector vecalpha into components with respect to vec aa n d vec b is given by a. 3 vec a-2 vec b b. 3 vec b-2 vec a c. 2 vec a-3 vec b d. vec a-2 vec b

The projection of the vector vec alpha=2hati+3hatj+2hatk on the vector vec beta=hati+2hatj+hatk is -

Let vec a , vec b and vec c be unit vectors such that vec a+ vec b- vec c=0. If the area of triangle formed by vectors vec a and vec b is A , then what is the value of 4A^2?

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) .