Question

If theta=30 degree prove that 4cos^3 theta -3 cos theta =cos3 theta​

Answer 1

Given : 4cos³θ-3cosθ = cos 3θ

To prove : The given Equation is true when θ = 30°

Solution :

We are aware that,

• cos 30° = √3/2
• cos 90° = 0

Consider LHS of given equation

LHS = 4 cos³θ - 3 cosθ

Put θ = 30°

LHS = 4 cos³ 30° - 3 cos 30°

LHS = 4 ( cos 30°)³ - 3 √3/2

LHS = 4 (√3/2)³ - 3√3/2

LHS = 4 × 3√3/8 - 3√3/2

LHS = 3√3/2 - 3√3/2

LHS = 0 _____(1)

Now consider RHS

RHS = cos 3θ

Put θ = 30°

RHS = cos ( 3 × 30° )

RHS = cos 90°

RHS = 0 ______(2)

From (1) and (2) required result is proved.