Considering L.H.S : Getting terms c – b cos A and b – c cos A from projection formula Using projection formula, \[c\text{ }=\text{ }a\text{ }cos\text{ }B\text{ }+\text{ }b\text{ }cos\text{...
For any Δ ABC show that (c2 – a2 + b2) tan A = (a2 – b2 + c2) tan B = (b2 – c2 + a2) tan C
Considering L.H.S : \[({{c}^{2}}~\text{ }{{a}^{2}}~+\text{ }{{b}^{2}}),\text{ }({{a}^{2}}~\text{ }{{b}^{2}}~+\text{ }{{c}^{2}}),\text{ }({{b}^{2}}~\text{ }{{c}^{2}}~+\text{ }{{a}^{2}})\] Using sine...
For any Δ ABC show that 2 (bc cos A + ca cos B + ab cos C) = a2 + b2 + c2
Considering L.H.S : \[2\text{ }\left( bc\text{ }cos\text{ }A\text{ }+\text{ }ca\text{ }cos\text{ }B\text{ }+\text{ }ab\text{ }cos\text{ }C \right)\] \[2ca\text{ }cos\text{ }B,\text{ }2ab\text{...
For any Δ ABC show that c (a cos B – b cos A) = a2 – b2
Considering L.H.S. \[c\text{ }\left( a\text{ }cos\text{ }B\text{ }\text{ }b\text{ }cos\text{ }A \right)\] \[ca\text{ }cos\text{ }B\text{ }and\text{ }cb\text{ }cos\text{ }A\] is present in L.H.S,...
For any ΔABC, show that b (c cos A – a cos C) = c2 – a2
So, considering LHS: \[b\text{ }\left( c\text{ }cos\text{ }A\text{ }\text{ }a\text{ }cos\text{ }C \right)\] \[bc\text{ }cos\text{ }A\text{ }and\text{ }ab\text{ }cos\text{ }C\]are L.H.S, which can be...
In a ∆ABC, if a = 18, b = 24, c = 30, find cos A, cos B and cos C
ACCORDING TO QUES,: Sides of a triangle are \[a\text{ }=\text{ }18,\text{ }b\text{ }=\text{ }24\text{ }and\text{ }c\text{ }=\text{ }30\] Hence, using the formulas: \[Cos\text{ }A\text{ }=\text{...
The sides of a triangle are a = 4, b = 6 and c = 8, show that: 8 cos A + 16 cos B + 4 cos C = 17.
ACCORDING TO QUES,: Sides of the triangle: \[a\text{ }=\text{ }4,\text{ }b\text{ }=\text{ }6\text{ }and\text{ }c\text{ }=\text{ }8\] By using the formulas, \[Cos\text{ }A\text{ }=\text{...
In a ∆ABC, if a = √2, b = √3 and c = √5 show that its area is1/2 √6 sq. units.
According to the given ques: In \[\vartriangle ABC,\text{ }a\text{ }=\text{ }\surd 2,\text{ }b\text{ }=\text{ }\surd 3\text{ }and\text{ }c\text{ }=\text{ }\surd 5~\] Hence, using the formulas,...
In a ∆ABC, if a = 5, b = 6 and C = 60o, show that its area is (15√3)/2 sq. units.
ACCORDING TO QUES: In a \[\vartriangle ABC,\text{ }a\text{ }=\text{ }5,\text{ }b\text{ }=\text{ }6\text{ }and\text{ }C\text{ }=\text{ }{{60}^{o}}\] By using the formula, Area of\[\vartriangle...