Question

sin4a+cos4a=1-2sin2a.cos2a​

Answer 1

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]

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Hope it helps