In `Delta ABC`, prove that `(a - b)^(2) cos^(2).(C)/(2) + (a + b)^(2) sin^(2).(C)/(2) = c^(2)`

In `Delta ABC`, prove that `(a - b)^(2) cos^(2).(C)/(2) + (a + b)^(2)

1.	In `Delta ABC`, prove that `(a - b)^(2) cos^(2).(C)/(2) + (a + b)^(2) sin^(2).(C)/(2) = c^(2)`
Answer» `L.H.S. = (a^(2) + b^(2) - 2ab) cos^(2).(C)/(2) + (a^(2) + b^(2) + 2 ab) sin^(2). (C)/(2)` `= a^(2) + b^(2) + 2ab (sin^(2).(C)/(2) - cos^(2).(C)/(2))` `= a^(2) + b^(2) - 2ab cos C` `= c^(2)` (Using consine Rule)

Discussion

No Comment Found

Related InterviewSolutions

If the angles of a triangle are in the ratio `4:1:1,`then the ratio of the longest side to the perimeter isA. `sqrt3 : (2 + sqrt3)`B. `1 : 6`C. `1 : 2 + sqrt3`D. `2 : 3`
A triangle with integral sides has perimeter 8 cm. Then find the area of the triangle
The area of the circle and the area of a regular polygon of `n`sides and of perimeter equal to that of the circle are in the ratio of`tan(pi/n):pi/n`(b) `cos(pi/n):pi/n``sinpi/n :pi/n`(d)`cot(pi/n):pi/n`A. `tan((pi)/(n)): (pi)/(n)`B. `cos ((pi)/(n)) : (pi)/(n)`C. `sin.(pi)/(n): (pi)/(n)`D. `cot((pi)/(n)): (pi)/(n)`
The sides of a triangle are in A.P. and its area is `(3)/(5)` th of an equilateral triangle of the same perimeter. Find the greatest angle of the triangle
In equilateral triangle ABC with interior point D, if the perpendiculardistances from D to the sides of 4,5, and 6, respectively, are given, thenfind the area of ` A B Cdot`
In `Delta ABC` if `AB = x, BC = x + 1, angleC = (pi)/(3)`, then the less integer value of x isA. 6B. 7C. 8D. none of these
In triangle ABC, `b^(2) sin 2C + c^(2) sin 2B = 2bc` where `b = 20, c = 21`, then inradius =A. 4B. 6C. 8D. 9
In `DeltaABC, R, r, r_(1), r_(2), r_(3)` denote the circumradius, inradius, the exradii opposite to the vertices A,B, C respectively. Given that `r_(1) :r_(2): r_(3) = 1: 2 : 3` The sides of the triangle are in the ratioA. `1 : 2 : 3`B. `3 : 5 : 7`C. `1 : 5 : 9`D. `5 : 8 : 9`
In `DeltaABC, R, r, r_(1), r_(2), r_(3)` denote the circumradius, inradius, the exradii opposite to the vertices A,B, C respectively. Given that `r_(1) :r_(2): r_(3) = 1: 2 : 3` The greatest angle of the triangle is given byA. `cos^(-1) ((1)/(30))`B. `cos^(-1)((1)/(3))`C. `cos^(-1)((1)/(10))`D. `cos^(-1) ((1)/(5))`
In `DeltaABC, R, r, r_(1), r_(2), r_(3)` denote the circumradius, inradius, the exradii opposite to the vertices A,B, C respectively. Given that `r_(1) :r_(2): r_(3) = 1: 2 : 3` The value of `R : r` isA. `5 : 2`B. `5 : 4`C. `5 : 3`D. `3 : 2`

In `Delta ABC`, prove that `(a - b)^(2) cos^(2).(C)/(2) + (a + b)^(2) sin^(2).(C)/(2) = c^(2)`

Discussion

No Comment Found

Related InterviewSolutions

Reply to Comment