" (20) "cos^(2)alpha+cos^(2)(t+190^(@))+cos^(2)(A-190^(@))=(3)/(2)

cos^(2)alpha+cos^(2)(alpha+120^(@))+cos^(2)(alpha-120^(@))=(3)/(2)

Show that, cos^(2)alpha + cos^(2) (120^(@) - alpha) + cos^(2) (120^(@) + alpha) = 3/2.

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

Prove that cos^2alpha+cos^2(120^@-alpha)+cos^2(120^@+alpha)=3/2

(cos^(2)alpha-cos^(2)beta)/(cos^(2)alpha*cos^(2)beta)=tan^(2)beta-tan^(2)alpha

To prove ((1)/(sec^(2)alpha-cos^(2)alpha)+(1)/(cos ec^(2)alpha-sin^(2)alpha))cos^(2)alpha sin^(2)alpha=(1-sin^(2)alpha cos^(2)alpha)/(2+sin^(2)alpha cos^(2)alpha)

((1)/(sec^(2)alpha-cos^(2)alpha)+(1)/(cos ec^(2)alpha-sin^(2)alpha))cos^(2)alpha*sin^(2)alpha=(1-cos^(2)alpha*sin^(2)alpha)/(2+cos^(2)alpha*sin^(2)alpha)

(cos2 x - cos2 alpha)/(cos x - cos alpha)