Question

sin raise to 8 theta minus Cos raise to 8 theta is equal to 1 - 2 cos square theta into 1 minus 2 sin square theta cos square theta​

Answer 1

Answer:

Proved

Step-by-step explanation:

sin raise to 8 theta minus Cos raise to 8 theta is equal to 1 - 2 cos square theta into 1 minus 2 sin square theta cos square theta​

to be proved

Sin⁸θ - Cos⁸θ = (1 - 2Cos²θ)(1 - 2Sin²θCos²θ)

LHS

= Sin⁸θ - Cos⁸θ

a² - b² = (a + b) (a-b)

here a = Sin⁴θ  & b = Cos⁴θ

= (Sin⁴θ + Cos⁴θ)(Sin⁴θ - Cos⁴θ)

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

Sin²θ + Cos²θ = 1

= (Sin⁴θ + Cos⁴θ)(1)(1 -Cos²θ - Cos²θ)

a² + b² = (a + b)² - 2ab

a = Sin²θ & b = Cos²θ

= ((Sin²θ + Cos²θ)² - 2Sin²θCos²θ)(1 - 2Cos²θ)

= (1² - 2Sin²θCos²θ)(1 - 2Cos²θ)

= (1 - 2Cos²θ)(1 - 2Sin²θCos²θ)

= RHS

QED

Answer 2

Step-by-step explanation:

hope you understood the answer