Cos 2 alpha cos 2 beta cos 2 gamma 1
Asked by admin @ in Physics viewed by 384 People
Prove cos^2 alpha + cos^2 beta + cos^2 gamma = 1
please help...
Asked by admin @ in Physics viewed by 384 People
Prove cos^2 alpha + cos^2 beta + cos^2 gamma = 1
please help...
Answered by admin @
it is based on concept of 3D - geometry. you know, direction cosine of a line is defined as thr angle made by lines with the positive direction of coordinate axes.
let a line r is made α, β and γ with X - axis, y-axis and z - axis respectively.
now component of r along x-axis is |r|cosα
similarly, component of r along y-axis is |r|cosβ
and component of r along x-axis is |r|cosγ
so we can write it in vector form,
i.e., r = |r|cosα i + |r|cosβ j + |r|cosγ k
now |r| = √{|r|²cos²α + |r|²cos²β + |r|²cos²γ}
⇒|r| = |r|√{cos²α + cos²β + cos²γ}
⇒1 = cos²α + cos²β + cos²γ
hence proved
also read similar questions : Prove that cos alpha+cos beta + cos gamma + cos (alpha+ beta + gamma) = 4 cos alpha + beta/2 cos beta +gamma/2 cos gamma...
sin alpha + beta minus , gamma equal to 1 by 2 cos beta + Gamma minus Alpha equal to 1 by 2 and tan alpha + beta minus, ...
Asked by admin @ in Math viewed by 269 persons
Asked by maham237 @ in Mathematics viewed by 338 persons
Asked by admin @ in Math viewed by 312 persons
Asked by admin @ in Math viewed by 300 persons
Asked by maham237 @ in Chemistry viewed by 311 persons
Asked by admin @ in Math viewed by 364 persons
Asked by admin @ in Biology viewed by 283 persons
Asked by admin @ in Math viewed by 298 persons
Asked by admin @ in Math viewed by 400 persons
Asked by admin @ in Chemistry viewed by 321 persons
Asked by maham237 @ in Mathematics viewed by 306 persons
Asked by admin @ in Math viewed by 353 persons
Asked by maham237 @ in Mathematics viewed by 294 persons
Asked by maham237 @ in Mathematics viewed by 239 persons
Asked by admin @ in Math viewed by 313 persons
Asked by admin @ in Physics viewed by 11082 persons
Asked by admin @ in Physics viewed by 2676 persons
Asked by admin @ in Physics viewed by 1536 persons
Asked by admin @ in Physics viewed by 1522 persons
Asked by maham237 @ in Physics viewed by 1324 persons
Asked by maham237 @ in Physics viewed by 1212 persons
Asked by admin @ in Physics viewed by 1153 persons
Asked by maham237 @ in Physics viewed by 1104 persons
Asked by maham237 @ in Physics viewed by 1087 persons