NEB Grade 12 | Trigonometry | Properties of Triangle | New Course Basic Mathematics Exercise Part 3
Автор: MRR Maths
Загружено: 2024-04-19
Просмотров: 1896
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0:0-3:09In any triangle, prove that:
(b−c)/a cos A/2=sin (B−C)/2
3:09-5:22 In any triangle, prove that:
5:22-10:20 bcos^2 A/2+acos^2 B/2=(a+b+c)/2
10:20-12:20 In any triangle, prove that:
a(cosB−cosC)=2(c−b)cos^2 A/2
12:20-12:21 In any triangle, prove that:
(b−c)/a cos^2 A/2+(c−a)/b cos^2 B/2+(a−b)/c cos^2 C/2=0
12:21-13:38 In any triangle, prove that:
bccos^2 A/2+cacos^2 B/2+abcos^2 C/2=𝑠^2
13:38-15:40 In any triangle, prove that:
tan^2 A/2 tan^2 B/2 tan^2 C/2=((𝑠−𝑎)/𝑠)((𝑠−𝑏)/𝑠)((𝑠−𝑐)/𝑠)
15:40-20:46 In any triangle, prove that:
(b+c−a)(cot B/2+cot C/2)=2acot A/2
20:46- 25:38 If a^4+b^4+c^4=2c^2 (a^2+b^2 ), Prove that C=45° or 135°
25:38-27:22 If (𝑎+𝑏+𝑐)(b+c−a)=3bc show that A=60°.
27:22-30:20 If 1/(a+c)+1/(b+c)=3/(a+b+c) show that C=60°.
30:20-32:13 If the cosines of two of the angles of a triangle are proportional to the
opposite sides, prove that the triangle is isosceles.
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