3 years ago

Prove the identity I NEED TO KNOW FAST AS POSSIBLE

Mathematics

1 answer:

antoniya [11.8K]3 years ago

5 0

Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identities

sin²Θ = 1 - cos²Θ , cos²Θ = 1 - sin²Θ

Consider the left side

(sinΘ + cosΘ)(1 - sinΘcosΘ) ← distribute

= sinΘ(1 - sinΘcosΘ) + cosΘ(1 - sinΘcosΘ)

= sinΘ - sin²ΘcosΘ + cosΘ - sinΘcos²Θ

= sinΘ - (1 - cos²Θ)cosΘ + cosΘ - sinΘ(1 - sin²Θ)

= sinΘ - cosΘ + cos³Θ + cosΘ - sinΘ + sin³Θ ← collect like terms

= sin³Θ + cos³Θ

= right side ⇒ proven

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