If A-B-C- show that sinA2-sinB2-sinC2 - 1-4sin- -A4sin- -B4sin- -C4-

L.H.S. =2sinA+B4cosA B4+cos(π2 C2) =2sinπ C4cosA B4+1 2sin^2π C4 =1+2sinπ C4[cosA B4 sinA+B4] by (1) =1+2sinπ C4[cosA B4 cos(π2 A+ ...

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Sin(A+B)Sin(A-B)

If A+B+C=π,...

Question

If $A + B + C = π$ , show that $sin (\frac{A}{2}) + sin (\frac{B}{2}) + sin (\frac{C}{2})$ = $1 + 4 sin \frac{π - A}{4} sin \frac{π - B}{4} sin \frac{π - C}{4}$ .

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A + B + C = π

s i n \frac{A}{2} + s i n \frac{B}{2} + s i n \frac{C}{2} - 1 = 4 s i n \frac{π - 4}{4} . s i n \frac{π - B}{4} . s i n \frac{π - C}{4}

\frac{\frac{π}{4} sin \frac{π}{4}}{sin \frac{π}{2} - sin \frac{π}{4}}

4 sin \frac{π}{6} {sin}^{2} \frac{π}{3} + 3 cos \frac{π}{3} tan \frac{π}{4} + {cosec}^{2} \frac{π}{2} = 2 {sec}^{2} \frac{π}{4}

A + B + C = π

(sin A + sin B + sin C) (- sin A + sin B + sin C) (sin A - sin B + sin C) (sin A + sin B - sin C) = 4 {sin}^{2} A {sin}^{2} B {sin}^{2} C

A + B + C = π

sin A + sin B - sin C = 2 sin \frac{A}{2} sin \frac{B}{2} cos \frac{C}{2}

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