Question

If tita=30 find cos3tita= 4 cos^3tita -3costita

Answer 1

CORRECT QUESTION :-

★ If ∅ = 30° then show that cos3∅ = 4cos³∅ - 3cos∅.

GIVEN :-

• ∅ = 30° .

TO SHOW :-

• cos3∅ = 4cos³∅ - 3cos∅.

SOLUTION :-

→ cos3∅ = 4cos³∅ - 3cos∅.

→ cos (3 × 30°) = 4cos³ 30° - 3cos30°

★ As we know that, cos30° = √3/2.

→ cos90° = 4 (cos³30°) - 3 × √3/2

★ As we know that, cos90° = 0

→ 0 = 4(√3/2)³ - 3√3/2

→ 0 = 4(√27/8) - 3√3/2

→ 0 = 3√3/2 - 3√3/2

→ 0 = 0

L.H.S = R.H.S

Hence verified ✅

ADDITIONAL INFORMATION :-

→ sin0° = 0

→ cos0° = 1

→ tan0° = 0

→ cot0° = ∞

→ cosec0° = ∞

Answer 2

Solution :-

$:\implies \sf \cos3 \theta = 4 { \cos}^{3} \theta - 3 \cos\theta \\ \\ :\implies \sf\cos3(30) \degree = 4 { \cos}^{3}(30) \degree - 3 \cos(30)\degree \\ \\:\implies \sf \cos90 \degree = 4 { \bigg(\frac{ \sqrt{3} }{2} \bigg) }^{3} - 3 \times \frac{ \sqrt{3} }{2} \\ \\:\implies \sf 0 = 4 \times \frac{ \sqrt{27} }{8} - \frac{ 3\sqrt{3} }{2} \\ \\:\implies \sf 0 = \frac{3 \sqrt{3} }{2} - \frac{3 \sqrt{3} }{2} \\ \\ :\implies \sf0 = 0$

LHS = RHS

Hence Proved