If A-B-C- then sin 2A-2-sin 2B-2-sin 2C-2-1-mcosA-2cosB-2cosC-2- Find m

sin ^2A/2+sin ^2B/2 sin ^2C/2=sin ( A+C/2 )sin ( A C/2 )+1 cos ^2B/2 #160; #160; #160; #160; #160; =cos ( B/2 )sin ( A C/2 ) cos ^2B/2+1 ...

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Byju's Answer

Standard XII

Mathematics

Definition of Functions

If A+B+C=π,...

Question

If $A + B + C = π$ , then ${sin}^{2} \frac{A}{2} + {sin}^{2} \frac{B}{2} - {sin}^{2} \frac{C}{2} = 1 - m cos \frac{A}{2} cos \frac{B}{2} cos \frac{C}{2}$ . Find $m$

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Solution

${sin}^{2} \frac{A}{2} + {sin}^{2} \frac{B}{2} - {sin}^{2} \frac{C}{2} = sin (\frac{A + C}{2}) sin (\frac{A - C}{2}) + 1 - {cos}^{2} \frac{B}{2}$

$= cos (\frac{B}{2}) sin (\frac{A - C}{2}) - {cos}^{2} \frac{B}{2} + 1$

$= cos (\frac{B}{2}) [sin (\frac{A - C}{2}) - cos \frac{B}{2}] + 1$

$= cos (\frac{B}{2}) [sin (\frac{A - C}{2}) - sin (\frac{A + C}{2})] + 1$

$= 1 - 2 cos \frac{A}{2} cos \frac{B}{2} cos \frac{C}{2}$
Ans: 2

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If A+B+C=π, then sin2A2+sin2B2−sin2C2=1−mcosA2cosB2cosC2. Find m

sin2A2+sin2B2−sin2C2=sin(A+C2)sin(A−C2)+1−cos2B2 =cos(B2)sin(A−C2)−cos2B2+1 =cos(B2)[sin(A−C2)−cosB2]+1 =cos(B2)[sin(A−C2)−sin(A+C2)]+1 =1−2cosA2cosB2cosC2Ans: 2

If $A + B + C = π$ , then ${sin}^{2} \frac{A}{2} + {sin}^{2} \frac{B}{2} - {sin}^{2} \frac{C}{2} = 1 - m cos \frac{A}{2} cos \frac{B}{2} cos \frac{C}{2}$ . Find $m$