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

Posted by Anushka Saha 7 years, 2 months ago

CBSE > Class 10 > Mathematics

4 answers

Neha Sirur 7 years, 2 months ago

Hope u ll get it

Yogita Ingle 7 years, 2 months ago

In a triangle, sum of all the interior angles
A + B + C = 180°
⇒ B + 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

Neha Sirur 7 years, 2 months ago

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

Anushka ? 7 years, 2 months ago

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.

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This content has been hidden. One or more users have flagged this content as inappropriate. Once content is flagged, it is hidden from users and is reviewed by myCBSEguide team against our Community Guidelines. If content is found in violation, the user posting this content will be banned for 30 days from using Homework help section. Suspended users will receive error while adding question or answer. Question comments have also been disabled. Read community guidelines at https://mycbseguide.com/community-guidelines.html

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