Question

I don't care about off my points I have many doubts so plzz solve one of them thanx have a prosperous new year

Answer 1

Answer:

1

Step-by-step explanation:

Given Equation is sin⁶θ + cos⁶θ + 3 sin²θ cos²θ

It can be written as,

⇒ (sin²θ)³ + (cos²θ)³ + 3(sin²θ)(cos²θ)[sin²θ + cos²θ]

We know that a³ + b³ + 3ab(a + b) = (a + b)³

⇒ (sin²θ + cos²θ)³

⇒ (1)³

⇒ 1.

------------------------------------- Happy New Year -----------------------------------------

Answer 2

Step-by-step explanation:

sin⁶θ + cos⁶θ

= (sin²θ)³ + (cos²θ)³

= (sin²θ + cos²θ)[(sin²θ)² - sin²θ cos²θ + (cos²θ)²]

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

= (1)[sin⁴θ - sin²θ cos²θ + cos⁴θ]

= (sin²θ)²+ (cos²θ)² - sin²θ cos²θ

= [(sin²θ)²+ 2 sin²θ cos²θ + (cos²θ)²] - 3 sin²θ cos²θ

= [sin²θ + cos²θ]² - 3 sin²θ cos²θ

= 1 - 3 sin²θ cos²θ

= R.H.S