Question

(sin theta -cos theta )²=1-2sin theta. cos theta prove it

Answer 1

(Sin theata-costheta)^2=sin^2theta+sin^2theta-2sin theta × cos theta

We know

sin^2theta+sin^2theta=1

So

(Sin theata-cos theta) ^2=1-2sin theta × cos theta

Answer 2

(a-b)^2= a^2-2ab+b^2 (equation 1)

(SinA-CosA)^2=1-2SinA. CosA

LHS = sinA^2-2sinACosA+Cos^2A(from equation1)

= 1 -2SinA. CosA(Sin^2A+Cos ^2A=1)

LHS=RHS