Question

Prove that sin4A-cos4A=1-2cos2A

Answer 1

Heya!
⇒sin^4A-cos^4A
⇒(sin²A)²-(cos²A)²
⇒(sin²A+cos²A )(sin²A-cos²A).
⇒(1)(1-cos²A-cos²A)
⇒1-2cos²A..

LHS=RHS
Hope this helps you ☺☺

Answer 2

HELLO DEAR,

GIVEN:-

sin⁴A - cos⁴A = 1 - 2cos²A

we know:- (a⁴ - b⁴) = (a² - b²)(a² + b²)

using this property,

we get,

(sin²A - cos²A)(sin²A + cos²A)

[as sin²θ + cos²θ = 1]

therefore, ( 1 ) *(sin²A - cos²A)

=> {(1 - cos²A) - cos²A}

=> (1 - 2cos²A) [hence, proved]

I HOPE ITS HELP YOU DEAR,

THANKS