If cos α+a cos β+b cos γ=0= sin α+a sin β+b sin γ then :

Question

If cos α+a cos β+b cos &gamma;=0= sin α+a sin β+b sin &gamma; then : (A)  cos 3 α+a3 cos 3 β+b3 cos 3 &gamma;=3 a b ⋅ cos (α+β+&gamma;) (B)  sin 3 α+a3 sin 3 β+b3 sin 3 &gamma;=3 a b ⋅ sin (α+β+&gamma;) (C) ei k Lambda+a ei β+b ei f=0 (D) e i (α+π / 2)+ ae i (β+π / 2)+ be i (&gamma;+π / 2)=0

Tardigrade Admin · Accepted Answer

Correct answer is (a) cos 3 α+a3 cos 3 β+b3 cos 3 &gamma;=3 a b ⋅ cos (α+β+&gamma;)Correct answer is (b) sin 3 α+a3 sin 3 β+b3 sin 3 &gamma;=3 a b ⋅ sin (α+β+&gamma;)Correct answer is (c) ei k Lambda+a ei β+b ei f=0Correct answer is (d) e i (α+π / 2)+ ae i (β+π / 2)+ be i (&gamma;+π / 2)=0

Q. If $cos α + a cos β + b cos γ = 0 = sin α + a sin β + b sin γ$ then :

$cos 3 α + a^{3} cos 3 β + b^{3} cos 3 γ = 3 ab \cdot cos (α + β + γ)$

$sin 3 α + a^{3} sin 3 β + b^{3} sin 3 γ = 3 ab \cdot sin (α + β + γ)$

$e^{ik Λ} + a e^{i β} + b e^{i f} = 0$

$e^{i (α + π /2)} + a e^{i (β + π /2)} + b e^{i (γ + π /2)} = 0$

Q. If cosα+acosβ+bcosγ=0=sinα+asinβ+bsinγ then :

cos3α+a3cos3β+b3cos3γ=3ab⋅cos(α+β+γ)

sin3α+a3sin3β+b3sin3γ=3ab⋅sin(α+β+γ)

eikΛ+aeiβ+beif=0

ei(α+π/2)+aei(β+π/2)+bei(γ+π/2)=0

Correct answer is (a) cos3α+a3cos3β+b3cos3γ=3ab⋅cos(α+β+γ) Correct answer is (b) sin3α+a3sin3β+b3sin3γ=3ab⋅sin(α+β+γ) Correct answer is (c) eikΛ+aeiβ+beif=0 Correct answer is (d) ei(α+π/2)+aei(β+π/2)+bei(γ+π/2)=0

Q. If $cos α + a cos β + b cos γ = 0 = sin α + a sin β + b sin γ$ then :

$cos 3 α + a^{3} cos 3 β + b^{3} cos 3 γ = 3 ab \cdot cos (α + β + γ)$

$sin 3 α + a^{3} sin 3 β + b^{3} sin 3 γ = 3 ab \cdot sin (α + β + γ)$

$e^{ik Λ} + a e^{i β} + b e^{i f} = 0$

$e^{i (α + π /2)} + a e^{i (β + π /2)} + b e^{i (γ + π /2)} = 0$