Prove that: (sin A - cosA)^2 = 1 - 2.sinA.cosA

Answer:


The given question is too simple. We have been learning the formula of
(a-b)^2 = a^2 - 2 a b + b^2

Applying the same formula for the given question, we get:
(sinA - cosA)^2 = sin^2A -2 sinA cosA + cos^2A

And we have the identity of:

sin^2A + cos^2A = 1

So, we get 1 in place of sin^2A + cos^2A  in
 sin^2A -2 sinA cosA + cos^2A

So, 1 - 2 sinA cosA is what we have finally!

Therefore the LHS is equal to he RHS.


#SciPiTutor
#TrigonometricIdentities
#Trigonometry
#Mathematics