[rArrquad sin^(2)alpha+sin^(2)beta+sin^(2)gamma=2],[" उदाहरण-3.बिन्दुओं "(1,0,0)" तथा "(0,1,1)" को जोड़ने वाली रेखा की दिक- कोसाइन ज्ञात कीजिए। "]

sin 2 alpha + sin 2 beta + sin 2 gamma - sin2(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 alpha,beta are roots of z^(2)sin^(2)theta-z sin2 theta+1=0 where '0

lim_(x rarr0)(sin(alpha+beta)x+sin(alpha-beta)x+sin2 alpha x)/(cos^(2)beta x-cos^(2)alpha x)

If A^(-1)=[(sin^2alpha,0,0),(0,sin^2 beta,0), (0,0,sin^2gamma)] and B^(-1)=[(cos^2alpha,0,0),(0,cos^2 beta,0), (0,0,cos^2gamma)] where alpha, beta, gamma are any real numbers and C=A^(-5)+B^(-5)+5A^(-1)B^(-1)(A^(-3) +B^(-3))+10 A^(-2)B^(-2)(A^(-1)+B^(-1)) then find |C|

If A^(-1)=[(sin^2alpha,0,0),(0,sin^2 beta,0), (0,0,sin^2gamma)] and B^(-1)=[(cos^2alpha,0,0),(0,cos^2 beta,0), (0,0,cos^2gamma)] where alpha, beta, gamma are any real numbers and C=A^(-5)+B^(-5)+5A^(-1)B^(-1)(A^(-3) +B^(-3))+10 A^(-2)B^(-2)(A^(-1)+B^(-1)) then find |C|

int_0^10([sin2pix])/e^(-[x]+x)dx=alphae^(-1)+betae^(-1/2)+gamma . then find alpha+beta+gamma

prove that | (sin alpha, sin beta, sin gamma), (cos alpha, cos beta, cos gamma), (sin 2alpha, sin 2beta, sin 2gamma) | = 4sin (1/2) (beta-gamma) * sin (1/2) (gamma-alpha) * sin (1/2) (alpha-beta) xx {sin (beta + gamma) + sin (gamma + alpha) + sin (alpha + beta)}.

If alpha+beta+gamma=0sin2 alpha+sin2 beta+sin2 gamma=lambda sin alpha sin beta sin gamma Find lambda.

If cos alpha+cos beta+cos gamma=0 and also sin alpha+sin beta+sin gamma=0 then prove that