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**Sine formula proof :Sine Rule**

**Problem on sine rule Type:-1(i) In a `DeltaABC` ; If `a=2;b=3 and sinA=2/3` ;find `/_B` (ii) In a `DeltaABC`; the angle of a triangle are in AP ; It is being given that `b:c=sqrt3:sqrt2`**

**An object is observed from three points `A, B,C` in the same horizontal line passing through the base of the object. The angle of elevation at `B` is twice and at `C` is thrice than that at `A`. If `AB=a, BC=b` prove that the height of the object is `h=(a/(2b))sqrt((a+b)(3b-a))` **

**The law of cosines proof :**

**In `Delta ABC` prove that (i)`a=bcosC+c cosB` (ii)` b=c cosA+acosC` (iii) `c=acosB+bcosA`**

**Half Angle Formula of `sin (A/2) ,Sin (B/2) ,sin(C/2)`**

**Half Angle Formula of `cos (A/2) ,cos (B/2), cos (C/2)`**

**Half Angle Formula of `tan(A/2), tan (B/2), tan (C/2)`**

**In any `DeltaABC` (i)`tan((B-C)/2)=((b-c)/(b+c))cot(A/2)` (ii) `tan((A-B)/2)=((a-b)/(a+b))cot(C/2)` (iii)`tan((C-A)/2)=((c-a)/(c+a))cot(B/2)`**

**Verify area of triangle is (i) `1/2 bc sin A` (ii) Herons Formula**