यदि किसी सरल रेखा की दिक् कोज्याएँ `cos alpha, cos beta , cos gamma ` हो , तो सिद्ध कीजिए कि
`cos 2 alpha +cos 2 beta +cos 2 gamma = -1 `

If cos alpha, cos beta, gamma are direciton cosines then cos 2 alpha + cos 2 beta + cos 2 gamma = ................

If alpha,beta ,gamma are direction angles of a line , then cos 2alpha + cos 2beta + cos 2 gamma =

cos alpha + cos beta + cos gamma + cos ( alpha + beta + gamma ) =

If cos alpha + cos beta + cos gamma = 0 = sin alpha + sin beta + sin gamma then (a) sin ^ (2) alpha + sin ^ (2) beta + sin ^ (2) gamma = (3) / ( 2) (b) sin ^ (2) alpha + sin ^ (2) beta + sin ^ (2) gamma = (3) / (4) (c) cos ^ (alpha) + cos ^ (2) beta + cos ^ (2) gamma = (3) / (2) (d) cos ^ (2) alpha + cos2 beta + cos2 gamma = -1

If cos alpha + cos beta + cos gamma = 0 = sin alpha + sin beta + sin gamma then cos ^ (2) alpha + cos ^ (2) beta + cos ^ (2) gamma is

If cos alpha+cos beta+cos gamma=0, then prove that cos3 alpha+cos3 beta+cos3 gamma=12cos alpha cos beta cos gamma

cos (alpha + beta) cos gamma-cos (beta + gamma) cos alpha = sin beta sin (gamma-alpha)

If |{:(1,cos alpha, cos beta),(cos alpha, 1 , cos gamma ),(cos beta, cos gamma , 1):}|=|{:(0,cos alpha, cos beta),(cos alpha , 0 , cos gamma),(cos beta, cos gamma, 0):}| then the value of cos^2 alpha + cos^2 beta + cos^2 gamma is : (a) 1 (b) 1/2 (c) 3/8 (d) 9/4

If |{:(1,cos alpha, cos beta),(cos alpha, 1 , cos gamma ),(cos beta, cos gamma , 1):}|=|{:(0,cos alpha, cos beta),(cos alpha , 0 , cos gamma),(cos beta, cos gamma, 0):}| then the value of cos^2 alpha + cos^2 beta + cos^2 gamma is : (a) 1 (b) 1/2 (c) 3/8 (d) 9/4