Question

prove that
sin^4A+cos^4A+sin^2Acos^2A=(1-sinAcosA)(1+sinAcosA)​

Answer 1

LHS

sin^4A + cos^4A + Sin^2Acos^2A

1 - 2sin^2Acos^2A + Sin^2Acos^2A

1 - Sin^2Acos^2A

(1-sinAcosA)(1+sinAcosA)

So LHS = RHS

Formula used

sin^4A + cos^4A = 1 - 2 sin^2ACos^2A

So

(sin^2A + cos^2A)^2= sin^4A + cos^4A +

2sin^2ACos^2A

1 - 2sin^2ACos^2A = sin^4A + cos^4A