If A-B-C-180o-sin 2A-sin 2B-sin 2C-sin A-sin B-sin C-k sinA-2sinB-2sinC-2- then the value of k is equal to

Given A+B+C=180^o, #10;sin #160;2A+sin #160;2B+sin #160;2C/sin #160;A+sin #160;B+sin #160;C=k sin #160;A/2sin #160;B/2sinC/2 #160; ...

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Sum of Trigonometric Ratios in Terms of Their Product

If A+B+C=18...

Question

If $A + B + C = 180^{o}, \frac{sin 2 A + sin 2 B + sin 2 C}{sin A + sin B + sin C} = k sin \frac{A}{2} sin \frac{B}{2} sin \frac{C}{2}$ , then the value of $k$ is equal to

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△ A B C

\frac{sin 2 A + sin 2 B + sin 2 C}{sin A + sin B + sin C} = k sin \frac{A}{2} sin \frac{B}{2} sin \frac{C}{2}

k

\frac{sin 2 A + sin 2 B + sin 2 C}{sin A + sin B + sin C} = 8 sin (\frac{A}{2}) sin (\frac{B}{2}) sin (\frac{C}{2})

A + B + C = 180^{\circ}

cos A + cos B + cos C

2 + 2 cos A cos B cos C

{sin}^{2} A + {sin}^{2} B + {sin}^{2} C

4 cos \frac{A}{2} cos \frac{B}{2} cos \frac{C}{2}

sin 2 A + sin 2 B + sin 2 C

1 + 4 sin \frac{A}{2} sin \frac{B}{2} sin \frac{C}{2}

sin A + sin B + sin C

4 sin A sin B sin C

x = y = z

sin A + sin B + sin C = {2 d}^{2}

sin 2 A + sin 2 B + sin 2 C = d^{2}

sin \frac{A}{2} sin \frac{B}{2} \frac{C}{2}

∣ ∣ ∣ ∣ \begin{matrix} s i n 2 A & s i n C & s i n B s i n C & s i n 2 B & s i n A s i n B & s i n A & s i n 2 C \end{matrix} ∣ ∣ ∣ ∣

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