sin^2A+cos^2A=1,then prove that sin^4-cos^4=1-sin^2A
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Solution :
sin²A + cos²A = 1 -----( 1 )
LHS = sin⁴A - cos⁴A
= (sin²A)² - ( cos²A )²
= (sin²A+cos²A)(sin²A - cos²A)
= sin²A - cos²A
= sin²A - ( 1 - sin²A )
= sin²A - 1 + sin²A
= 2sin²A - 1
•••••
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