Question

Show that r+r3+r1-r2=4RcosB​

Answer 1

Answer:

My handwriting is not good but I hope it will be help full for you

Answer 2

Proved that r+r3 +r – r2 = 4R

Cos B

Given

To prove that r +r3+ri - r2 = 4R

Cos B

Let us take, r +r3 = 4R

sinC sinA sinb +cosA , cosB) 2( sin

(1)

= 4sin cos 4,B

ri - r2 = 4R sin \frac{C}

(2}}[ sin sin + cos cos ]

= 4r Cos, sin (4-B) (2)

Add the equation (1) and ( 2 ) to get the desired result,

r r3 + r – r2

= 4Rsin cos 4B +

4 Cos, sin (4,B)

Add the equation (1) and ( 2 ) to get the desired result,

r + r3 +ri – r2

= 4Rsin cos4 B +

4cos sin ^z" 2

C = 4Rsin 2 A 2 B 2 + +

= 4 Sin(90 – - 5) B 2

= 4Rsin(90 – 25)

sin (90° - B) = cos B )

4R cos B. =

Hence, proved.