Question

If a+b+c=180 then prove that cot^2 A/2+cos^2 B/2+cos^2C/2=2+2sinA/2sinB/2sinC/2

Answer 1

Explanation:

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Forum Trigonometry Sin²A/2+sin²B/2+sin²C/2=1-2sinA/2sinB/2sinC/...

Sin²A/2+sin²B/2+sin²C/2=1-2sinA/2sinB/2sinC/2

Need to prove this formula

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Rashna kabir, 2 years ago

Grade:12

1 Answers

Arun

25763 Points

2 years ago

given A+B+C=180

LHS SIN²A/2+SIN²B/2+SIN²C/2

1/2(2SIN²A/2+2SIN²B/2+2SIN²C/2)

1/2(1-COSA+1-COSB+1-COSC)

1/2(3-(COSA+COSB+COSC)

1/2(3- (2COS (A+B/2)COS(A-B/2)+COSC)

1/2(3- (2COS(90-C/2)COS(A+B/2)+C0SC)

1/2(3- (2SINC/2COS(A-B/2)+1-2SIN²C/2)

1/2(3-1-2SINC/2(COS(A+B/2)-SINC/2)

1/2(2-2SINC/2(COS(A-B/2)-SIN (90-A+B/2) (SIN90-Ф)= COSФ)

1/2(2-2SINC/2(COS(A-B/2)-COS(A+B/2)

1/2(2-2SINC/2(2SINA/2SINB/2)

1/2(2-4SINA/2SINB/2SINC/2)

1-2SINA/2SINB/2SINC/2

RHS