" If the vectors "bar(b)=(tan alpha,-1,sqrt(4sin((alpha)/(2)))),bar(c)=[tan alpha,tan alpha,(-3)/(sqrt(sin(alpha/2)))]" are orthogonal and the vector "bar(a)=(1,3,sin2 alpha)

If the vectors barb=(tan alpha, -1, sqrt(4"sin"(alpha)/(2))), barc=(tan alpha, tan alpha, (-3)/(sqrt("sin"(alpha)/(2)))) are orthogonal and the vector bara=(1,3, sin 2alpha) makes an obtuse angle with Z-axis then alpha=

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 a alpha=tan^(-1)2 b. alpha=-tan^(-1)2 c. alpha=tan^(-1)2 d. alpha=tan^(-1)2

If the vectors vecb = tanalpha hati = hatj+2, sqrt(sinalpha/2hatk) , and vecc=tan alpha hati + tan alpha hatj-3/sqrt(sin alpha/2)hatk are orthogonal and a vector veca = hati + 3hatj + sin 2alpha hatk makes an obtuse angle with the z-axis, then the value of alpha is

(1-2sin^(2)alpha)/(1+sin2 alpha)=(1-tan alpha)/(1+tan alpha)

(1-2sin^(2)alpha)/(1+sin2 alpha)=(1-tan alpha)/(1+tan alpha)

sin alpha=(1)/(2)sqrt(a)sin^(alpha)alpha-4sin^(3)alpha

In R^(2) , find the unit vector orthogonal to unit vector bar(x) = ( cos alpha , sin alpha )

If cos alpha=(3)/(5), then value of (sin alpha-(1)/(tan alpha))/(2tan alpha) is

(sin^(2)alpha)/(1+cot^(2) alpha) + (tan^(2)alpha)/((1+tan^(2) alpha)^(2)) + cos^(2) alpha =

If tan alpha=(sqrt(3)+1)/(sqrt(3)-1) then the expression cos2 alpha+(2+sqrt(3))sin2 alpha is