Home
Class 12
MATHS
If A,B,C be anlges of a triangle, then p...

If A,B,C be anlges of a triangle, then prove that, `|{:(-1,cosC,cosB),(cosC,-1,cosA),(cosB,cos A,-1):}|=0`

Text Solution

Verified by Experts

The correct Answer is:
`=-sin^2A+sin^2A[because sin (B+c)=sin A] =0 `
Promotional Banner

Topper's Solved these Questions

  • DETERMINANT

    CHHAYA PUBLICATION|Exercise EXERCISE 2A|36 Videos
  • DETERMINANT

    CHHAYA PUBLICATION|Exercise EXERCISE 2B|111 Videos
  • DEFINITE INTEGRAL AS AN AREA

    CHHAYA PUBLICATION|Exercise Assertion-Reason Type|2 Videos
  • DIFFERENTIAL EQUATIONS OF THE FIRST ORDER AND FIRST DEGREE

    CHHAYA PUBLICATION|Exercise E ASSERTION-REASON TYPE|2 Videos

Similar Questions

Explore conceptually related problems

If A,B,C be the angles of a triangle, then prove that , abs((-1,cosC,cosB),(cosC,-1,cosA),(cosB,cosA,-1)) =0

If A , Ba n dC are the angels of a triangle, show that |[-1+cos B, cos C+cos B, cos B],[ cos C+cos A,-1+cos A ,cos A],[-1+cos B,-1+cos A,-1]|=0

Prove that a(bcosC-c cosB)=b^2-c^2

If A+B+C=180^@ , then prove that cos2A + cos2B +cos2C=-1-4cosA cosB cosC .

In a triangle ABC , if a,b,c are the sides opposite to angles A , B , C respectively, then the value of |{:(bcosC,a,c cosB),(c cosA,b,acosC),(acosB,c,bcosA):}| is

For any triangle ABC prove that acosA+bcosB +c cosC=2a sinBsinC

prove that cosA +cosB+cosC=1+r/R.

If A+B+C= pi ,prove that :cosA+cosB-cosC=-1+4cosA/2cosB/2sinC/2.

Prove that (sin A+sinB)/(cosB-cosA)=(cos A+cosB)/(sinA-sinB) .

In A B C , prove that cosA+cosB+cosClt=3/2dot