Question

Prove that sinA-cosA square=1-sin2A

Answer 1

LHS
= (sin A - cos A)^2
= sin^2 A + cos^2 A - 2 sin A cos A
= 1 - 2 sin A cos A
because sin^2 x + cos^2 x = 1

so,
= 1 - 2sinAcosA
= 1- sin2A because sin 2A = 2sinAcosA

= 1 - sin 2A = RHS

Answer 2

Answer:

LHS=

sin²A + cos²A - 2sinAcosA

1-2sinAcosA

1-2[sin2A/2]

⇒1-sin2A         (because sinAcosA = sin2A/2)