Answer :

Given: sin θ – cos θ = 1 …….(1)


cos θ + sin θ = 1 …….(2)


Square equation (1) and (2) on both sides:


sin2 θ + cos2 θ – 2 cos θ sin θ = 1 …….(3)


cos2 θ + sin2 θ + 2 cos θ sin θ = 1 ……..(4)


Add equation (3) and (4):


(sin2 θ + cos2 θ) + (sin2 θ + cos2 θ) = 1+1


(1) + (1) = 2


+ = 2


Hence, proved.


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