If theta=30 degree prove that 4cos^3 theta -3 cos theta =cos3 theta
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If theta=30 degree prove that 4cos^3 theta -3 cos theta =cos3 theta
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Given : 4cos³θ-3cosθ = cos 3θ
To prove : The given Equation is true when θ = 30°
Solution :
We are aware that,
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.