Which of the following relations is true for two unit vector A ^ and B ^ making an angle θ to each other?

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We know, 1 - cos θ = 2 sin 2 θ 2 1 + cos θ = 2 cos 2 θ 2 Now, a → + b → · a → + b → = a → 2 + 2 a → · b → + b → 2 ⇒ a → + b → · a → + b → = 1 2 + 2 × 1 × 1 × cos θ + 1 2 ⇒ a → + b → · a → + b → = 2 1 + cos θ ⇒ a → + b → 2 = 4 cos 2 θ 2 ⇒ a → + b → = 2 cos θ 2 . . . ( 1 ) Similarly, a → - b → · a → - b → = a → 2 - 2 a → · b → + b → 2 ⇒ a → - b → · a → - b → = 1 2 - 2 × 1 × 1 × cos θ + 1 2 ⇒ a → - b → · a → - b → = 2 1 - cos θ ⇒ a → - b → 2 = 4 sin 2 θ 2 ⇒ a → - b → = 2 sin θ 2 . . . ( 2 ) Therefore, A ^ - B ^ = A ^ + B ^ tan θ 2

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