Question

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If A, B, and C r interior angles of a triangle ABC then show that Sin B+C/2 = Cos A/2​​

Answer 1

GIVEN

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• A, B and C are interior angles of a triangle ABC⠀

⠀

TO PROVE

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• sin{(B + C)/2} = cosA/2

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SOLUTION

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• ⟶ (A + B + C )/2 = 90

• ⟶ B/2 + C/2 = 90 – A/2

• ⟶ sin(B + 2)/2 = sin(90 – A/2)

• ⟶ sin(B + C)/2 = cosA/2

⠀⠀⠀⠀⠀⠀⠀L.H.S = R.H.S

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀__Hence proved

Answer 2

Step-by-step explanation:

(A + B + C )/2 = 90

B/2 + C/2 = 90 – A/2

sin(B + 2)/2 = sin(90 – A/2)

sin(B + C)/2 = cosA/2

⠀⠀⠀⠀⠀⠀⠀L.H.S = R.H.S

HOPE this helps ☺️