Prove (sin(x) - cos(x))2 + (sin(x) + cos(x))2 = 2

Here is the step by step demonstrations to prove (sin(x) - cos(x))2 + (sin(x) + cos(x))2 = 2 trig identity easily.


(sin(x) - cos(x))2 + (sin(x) + cos(x))2 = 2 - Trig Identities Proof

LHS
= (sin(x) - cos(x))2 + (sin(x) + cos(x))2

= [ sin2(x) + cos2(x) - 2 sin(x) cos(x) ] + [ sin2(x) + cos2(x) + 2 sin(x) cos(x) ]

= 2 (sin2(x) + cos2(x))

= 2

= RHS

Hence Proved.
Trig identities proof are made simpler and easier here. Listed here various trig identities with the step by step proof.


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