Please wait...
1800-212-7858 (Toll Free)
9:00am - 8:00pm IST all days

or

Thanks, You will receive a call shortly.
Customer Support

You are very important to us

For any content/service related issues please contact on this toll free number

022-62211530

Mon to Sat - 11 AM to 8 PM

In a triangle, if 
 
 
       1                   1                    1
 
   1+sin A          1+sin B            1+sinC        =0
 
  sinA+Sin2A    sinB+Sin2B     SinC+Sin2C
 
 
 
then using the property of determinant prove that the triangle is  an   isosceles triangle

Asked by ppratim02 5th July 2016, 9:30 PM
Answered by Expert
Answer:
begin mathsize 12px style open vertical bar table row 1 1 1 row cell 1 plus sinA end cell cell 1 plus sinB end cell cell 1 plus sinC end cell row cell sinA plus sin squared straight A end cell cell space space space space space space sinB plus sin squared straight B end cell cell space space space space space space space sinC plus sin squared straight C end cell end table close vertical bar equals 0
straight C subscript 2 rightwards arrow straight C subscript 2 minus straight C subscript 1
rightwards double arrow open vertical bar table row 1 0 1 row cell 1 plus sinA end cell cell sinB minus sinA end cell cell 1 plus sinC end cell row cell sinA plus sin squared straight A end cell cell space space space space space space sinB plus sin squared straight B minus sinA minus sin squared straight A end cell cell space space space space space space space sinC plus sin squared straight C end cell end table close vertical bar equals 0
straight C subscript 3 rightwards arrow straight C subscript 3 minus straight C subscript 1
rightwards double arrow open vertical bar table row 1 0 0 row cell 1 plus sinA end cell cell sinB minus sinA end cell cell sinC minus sinA end cell row cell sinA plus sin squared straight A end cell cell space space space space space space sinB plus sin squared straight B minus sinA minus sin squared straight A end cell cell space space space space space space space sinC plus sin squared straight C minus sinA minus sin squared straight A end cell end table close vertical bar equals 0
rightwards double arrow open vertical bar table row 1 0 0 row cell 1 plus sinA end cell cell sinB minus sinA end cell cell sinC minus sinA end cell row cell sinA plus sin squared straight A end cell cell space space space space space space left parenthesis sinB plus sinA right parenthesis left parenthesis sinB minus sinA right parenthesis plus left parenthesis sinB minus sinA right parenthesis end cell cell space space space space space space space left parenthesis sinC plus sinA right parenthesis left parenthesis sinC minus sinA right parenthesis plus left parenthesis sinC minus sinA right parenthesis end cell end table close vertical bar equals 0
rightwards double arrow left parenthesis sinB minus sinA right parenthesis left parenthesis sinC minus sinA right parenthesis open vertical bar table row 1 0 0 row cell 1 plus sinA end cell 1 1 row cell sinA plus sin squared straight A end cell cell space space space space space space left parenthesis sinB plus sinA right parenthesis plus 1 end cell cell space space space space space space space left parenthesis sinC plus sinA right parenthesis plus 1 end cell end table close vertical bar equals 0
rightwards double arrow left parenthesis sinB minus sinA right parenthesis left parenthesis sinC minus sinA right parenthesis left square bracket space left parenthesis sinC plus sinA right parenthesis plus 1 minus space left parenthesis sinB plus sinA right parenthesis minus 1 right square bracket equals 0
rightwards double arrow left parenthesis sinB minus sinA right parenthesis left parenthesis sinC minus sinA right parenthesis left square bracket sinC plus sinA right parenthesis minus space sinB minus sinA right square bracket equals 0
rightwards double arrow left parenthesis sinB minus sinA right parenthesis left parenthesis sinC minus sinA right parenthesis left parenthesis sinC minus space sinB right parenthesis equals 0
rightwards double arrow sinB minus sinA equals 0 space space or space space sinC minus sinA equals 0 space space or space space sinC minus space sinB equals 0
rightwards double arrow sinB equals sinA space space space or space space sinC equals sinA space space space or space space sinC equals space sinB
rightwards double arrow straight B equals straight A space or space straight C equals straight A space or space straight C equals straight B
Hence comma space increment ABC space is space an space isosceles space triangle.
end style
Answered by Expert 7th July 2016, 10:29 AM
Rate this answer
  • 1
  • 2
  • 3
  • 4
  • 5
  • 6
  • 7
  • 8
  • 9
  • 10

You have rated this answer /10

Your answer has been posted successfully!

Chat with us on WhatsApp