Question

prove that sec4A-cos4A=1-2cos2A

Answer 1

HELLO DEAR,

YOUR QUESTIONS IS--------------prove that:- sin⁴A - cos⁴A = 1 - 2cos²A

TO PROVE:-

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