Question

Prove that (sin^8A-cos^8A)=(2sin^2A–1)(1-2sin^2Acos^2A)

Answer 1

To prove :

sin⁸A - cos⁸A

= (2 sin²A - 1)(1 - 2 sin²A cos²A)

Proof :

Now, sin⁸A - cos⁸A

= (sin⁴A - cos⁴A) (sin⁴A + cos⁴A)

= (sin²A + cos²A) (sin²A - cos²A)

{(sin²A + cos²A)² - 2 sin²A cos²A}

= {sin²A - (1 - sin²A)} (1 - 2 sin²A cos²A)

= (sin²A - 1 + sin²A) (1 - 2 sin²A cos²A)

= (2 sin²A - 1) (1 - 2 sin²A cos²A)

⇒ sin⁸A - cos⁸A

= (2 sin²A - 1) (1 - 2 sin²A cos²A)

Hence, proved.

Trigonometric Rules :

• sin²A + cos²A = 1

• sec²A - tan²A = 1

• cosec²A - cot²A = 1

Answer 2

Answer:

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Step-by-step explanation:

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