Question

How do you verify `(sinA-cosA)^2=1-2sin^2AcotA`?

Answer 1

see below

Explanation:

`(sinA-cosA)^2=1-2sin^2AcotA`

`(sinA-cosA)(sinA-cosA)=1-2sin^2A*cosA/sinA`

`sin^2A-2sinAcosA+cos^2A=1-2sin^cancel2AcosA/cancelsinA`

`sin^2A+cos^2A-2sinAcosA=1- 2 sinA cos A`

`1-2 sin A cos A=1- 2 sinA cos A`

`:.`Left Hand Side = Right Hand Side