Question

06). If x= 30° verify that
cos 3x = 4cos^3 x - 3 cosx
​

Answer 1

$\orange\boxed{QUESTION}$

If x = 30°

verify that , cos 3 x = 4 cos³ x - 3 cos x.

$\blue\boxed{knowledge\:required}$

value of cos 30° = √3 / 2

value of cos 90° = 0

$\green\boxed{SOLUTION}$

substituting x = 30° in LHS

we will get,

LHS = cos 3 (30°) = cos 90° = 0

now, substituting x = 30° in RHS

RHS = 4 cos³*30° - 3 cos 30°

RHS = 4 (√3/2)³ - 3 ( √3 / 2 )

RHS = 4 ( 3√3 / 8 ) - (3√3 / 2)

RHS = ( 3√3/2) - (3√3/2)

RHS = 0

$\yellow{LHS=RHS}\\\\hence proved.$

Answer 2

Answer:

yes we can verify the given equation

Step-by-step explanation:

given

x=30°

let l.h.s= cos 3 x ⇒ cos(3*30)⇒ cos 90°=0

     r.h.s=4 cos^3 x -3 cos x

⇒x=30°

⇒4 (cos 30°)^3-3 cos 30

=4(√3/2)^3- 3*(√3/2 )

=(4*√3/2*√3/2*√3/2) -  3√3/2

⇒3√3/2-3√3/2

=0

l.h.s=r.h.s=0

∴cos 3 x = 4 cos^3 x- 3 cos x is proved where x= 30°