Prove That: Sin6θ + Cos6θ = 1 - 3sin2θ Cos2θ.

Prove that: sin⁶θ + cos⁶θ = 1 - 3sin²θ cos²θ.

Sum

sin⁶θ + cos⁶θ
= (sin²θ)³ + (cos²θ)³

= (sin²θ + cos²θ)(sin⁴θ + cos²θ - sin²θcos²θ)

= 1 x [(sin²θ)² + (cos²θ)²+ 2sin²θ.cos²θ - 3sin²θ.cos²θ]

= (sin²θ)² + (cos²θ)² - 3sin²θ.cos²θ

= 1 - 3sin²θ cos²θ.

= RHS

shaalaa.com

Is there an error in this question or solution?

9 sec² A − 9 tan² A = ______.

Prove the identity (sin θ + cos θ)(tan θ + cot θ) = sec θ + cosec θ.

Prove the following trigonometric identities.

`sin A/(sec A + tan A - 1) + cos A/(cosec A + cot A + 1) = 1`

Prove that:

`(sinA - cosA)(1 + tanA + cotA) = secA/(cosec^2A) - (cosecA)/(sec^2A)`

What is the value of (1 − cos² θ) cosec² θ?

Prove that sin( 90° - θ ) sin θ cot θ = cos²θ.

Prove that `(tan^2 theta - 1)/(tan^2 theta + 1)` = 1 – 2 cos²θ

The value of the expression [cosec(75° + θ) – sec(15° – θ) – tan(55° + θ) + cot(35° – θ)] is ______.

(1 + sin A)(1 – sin A) is equal to ______.

Prove the following trigonometry identity:

(sin θ + cos θ)(cosec θ – sec θ) = cosec θ ⋅ sec θ – 2 tan θ