Home/ Questions/Q 263812
Next
In Process
Jobin Narayanan
Asked: 2022-11-05T11:55:55+05:30 In:

If A,B and C are interior angles of triangle ABC,then show that cos(B+C/2)=sinA/2

If A,B and C are interior angles of triangle ABC,then show that cos(B+C/2)=sinA/2
Leave an answer

Leave an answer

Browse

1 Answer

  1. A+B+C = 180°B+C=180°-AB+C/2=90°-A/2Cos(B+C/2)=cos(90°-A/2)Cos(B+C/2)=sin(A/2)Hence proved

    • 0
Nitin Yohannan
Asked: 2022-10-29T01:27:55+05:30 In:

If A, B and C are interior angles of triangle ABC then show that cos(B+C/2)=sinA/2

If A, B and C are interior angles of triangle ABC then show that cos(B+C/2)=sinA/2
Leave an answer

Leave an answer

Browse

1 Answer

  1. Hope u ll get it
    In a triangle, sum of all the interior anglesA + B\xa0+ C = 180°⇒ B\xa0+ C = 180° – A⇒ (B+C)/2 = (180°-A)/2⇒ (B+C)/2 = (90°-A/2)⇒ sin (B+C)/2 = sin (90°-A/2)⇒ sin (B+C)/2 = cos A/2
    In a triangle abc we know that all three angles is equal to 180° so angle a +b+c=180. Now shift a on the other side i.e. b+c=180-a next divide both sides by 2 so it gives (b+c) /2= 90-a/2. further on put cos on both sides —. Cos (b+c)/2= cos 90-a/2 and cos 90-a/2 = sin a/2. So substitute it and we get cos (b+c)/2 = sin a/2
    Cos(B+C/2) CAN BE WRITTEN AS Sin(90-B+C/2)…by taking the L. C. M, we will get Sin(180-B+C/2) and we know that in a triangle 180-B+C/2 is equal to A . So, our answer will be SinA/2.

    • 0