How many of the following relations are correct?

(1)1. Sin(A+B) = sinAcosB + cosAsinB

(2)2. cos(A-B) = CosAcosB - sinAsinB

(1)3. Tan (A-B) = $\frac{t a n A - t a n B}{1 + t a n A t a n B}$

(2)4. Sin(A+B) (sin(A-B) = $c o s^{2} A - c o s^{2} B$

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Solution

(1) and (3) are correct.

(2) cos (A-B) = cosAcosB+sinAsinB

(4) sin(A+B) sin(A-B) = $s i n^{2} A - s i n^{2} B$

= $c o s^{2} B - c o s^{2} A$

Key steps concepts: (1) Remembering the formula

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