Question

Cos power 6 theta - sin power 6 theta = cos2theta into 1-1/4 sin square theta

Answer 1

Answer:

Step-by-step explanation:

Cos⁶θ - Sin⁶θ

= (Cos²θ )³ - (Sin²θ)³

//a³ - b³ = (a-b)(a²+ab+b²)

= (Cos²θ - Sin²θ)(Cos⁴θ +Cos²θSin²θ+ Sin⁴θ)

=  (Cos²θ - Sin²θ)(Cos⁴θ +Sin⁴θ + Cos²θSin²θ)

= Cos2θ[(Cos²θ+Sin²θ)² - 2Cos²θSin²θ + Cos²θSin²θ]

= Cos2θ[1 - Cos²θSin²θ]

= Cos2θ[1 - (2CosθSinθ)²/4]

= Cos2θ [ 1 - 1/4*Sin²2θ]

= R.H.S

Hence proved.