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Ex 8.3, 6 - Show that sin (B + C / 2) = cos A/2 - Ex 8.3

  1. Chapter 8 Class 10 Introduction to Trignometry
  2. Serial order wise
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Ex 8.3, 6 If A, B and C are interior angles of a triangle ABC, then show that sin ((B + C)/2)= cos ๐ด/2 In ฮ” ABC Sum of angles of a triangle = 180 ยฐ A + B + C = 180ยฐ B + C = 180ยฐ โ€“ A Multiplying both sides by 1/2 (๐ต + ๐ถ)/2 " = " (180ยฐ โˆ’ ๐ด)/2 (๐ต + ๐ถ)/2 " = " (180ยฐ)/2 โ€“ ๐ด/2 (๐ต + ๐ถ)/2 " = " 90ยฐ โ€“ ๐ด/2 Taking L.H.S sin ((๐ต + ๐ถ)/2) = sin ("90ยฐ โˆ’ " ( ๐ด)/2) = ๐‘๐‘œ๐‘  ๐ด/2 = R.H.S Hence proved

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