IIT JEE , AIEEE Forum - Mathematics , Vectors

manjotpahwa

using vectors prove that

sin(a+b)= sina*cosb + cosa*sinb

sandeepramesh

hint:

consider a unit circle and projections of a vector from its origin

layman

Let the two vectors be a and b on a unit circle.

a=cos A i + sin A j

b=cos B i + sin B j

|axb|=sin A.cos B+cos A.sin B = |a|.|b|.sin(A+B)

=>sin(A+B) = sin A.cos B+cos A.sin B

arpan1

someone pls post this type of related ques,...

i need them badly

layman

Try proving cos(A-B)=cos A.cos B+sin A.sin B

layman

Similar type only

arpan1

pls post some more

pottermania1990

in that case a and b must b in the same quadrant with A>B

arpan1

hey someone post more ques. of this type

multiple rates assured

layman

1.Prove angle in a semicircle is 90.

2.Prove that in a rhombus diagonals bisect each other at right angles.

ramkumar_november

here are my questions:::

1 . prove sine rule using vectors

$\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}$

2 . prove using vectors $cosA=\frac{b^2+c^2-a^2}{2bc}$

3. THIS IS A REALLY GOOD SUM

prove Hero's formula using vectors

$Area= \sqrt{s(s-a)(s-b)(s-c)}$

where a,b,c are sides of the triangle.......

layman

I started a new thread for this