Question

Sin6theta-cos6theta

Answer 1

Answer:

sin0teta and cos tetha

Answer 2

$Sin^{6}$θ - $Cos^{6}$θ = = - cos2θ  $\frac{1}{4}$ (4 - sin²2θ)

$Sin^{6}$θ - $Cos^{6}$θ

= ($Sin^{6}$θ) - ($Cos^{6}$θ)

= (sin²θ)³ - (cos²θ)³

From Formula, a³ - b³ = (a - b)(a² + b² + ab )

= (sin²θ - cos²θ)(sin⁴θ+ cos⁴θ+ sin²θ cos²θ)

= - (cos²θ- sin²θ) {(sin²θ + cos²θ)² - 2 sin²θ cos²θ + sin²θ cos²θ}

= - cos2θ { 1 - $\frac{1}{4}$ (2 sinθ cosθ)²}

= - cos2θ $\frac{1}{4}$ (4 - sin²2θ)

[By using, cos²θ - sin²θ = cos2θ , 2sinθ cosθ = sin2θ ]

Know More

Q.1.- If cos θ+ sin θ=√2 cos θ, show that cos θ-sin θ=√2 sin θ

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Q.2.- What is cos²θ-sin²θ and -sin²θ+cos²θ​

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