Prove cos (3x) = 4cos³ (x) -3cos (x)

Trigonometry helps in finding the measure of unknown dimensions of a right-angled triangle using formulas and identities based on this relationship.

Answer: Hence proved that cos (3x) = 4cos³x−3cosx

We have to prove cos (3x) = 4cos³x−3cosx

Expanantion :

We know that, 

cos(A+B) = cos(A)cos(B) - sin(A)sin(B)

We can write cos(3x) = cos(2x + x)

Using the formula let's solve LHS = cos(3x)

cos(2x + x) = cos2x cosx − sin2x sinx                   

= (−1+2cos²x) cosx − (2cosx sinx) sinx       (Since, cos2x = -1 + 2cos²x and sin2x = 2cosx sinx)

= − cosx + 2 cos³x − 2sin²x cosx

= − cosx + 2cos³x − 2(1 − cos²x)cosx      (Since, sin²x = 1 - cos²x)

= − cosx + 2 cos³x - 2cosx + 2 cos³x

= 4cos³x − 3cosx = RHS

Thus, verified cos (3x) = 4cos³x − 3cosx