Question

if theta = 30° prove that 4cos^2 theta -3 cos theta = cos 3 theta​

Answer 1

Correct Question :- if theta = 30° prove that 4cos^3 theta - 3 cos theta = cos 3 theta.

Given :- theta = 30°

To prove :- 4cos^³ theta - 3 cos theta = cos 3 theta.

Proof :-

Consider LHS,

→ 4cos³(θ) - 3cos(θ)

→ 4cos³(30°) - 3cos(30°)

we know that, the value of cos(30°) = √3/2.

→ 4(√3/2)³ - 3(√3/2)

→ 4 * 3√3/8 - 3√3/2

→ 3√3/2 - 3√3/2

→ 0

Now, consider RHS,

→ cos3θ

given that, θ = 30°, putting θ = 30° in the equation, we get:

→ cos(3 * 30°)

→ cos(90°)

we know that, the value of cos(90°) = 0.

→ 0

Hence, from here we can conclude that, LHS = RHS.

Extra knowledge :-

Trigonometric ratios are sin, cos, tan, cot, sec, cosec.

The standard angles of these trigonometric ratios are 0°, 30°, 45°, 60° and 90°.